Journal of Mathematics of Kyoto University最新文献

{"title":"A Gauss-Bonnet-type formula on Riemann-Finsler surfaces with nonconstant indicatrix volume","authors":"J. Itoh, S. Sabau, H. Shimada","doi":"10.1215/0023608X-2009-008","DOIUrl":"https://doi.org/10.1215/0023608X-2009-008","url":null,"abstract":"We prove a Gauss-Bonnet type formula for Riemann-Finsler surfaces of non-constant indicatrix volume and with regular piecewise smooth boundary. We give a Hadamard type theorem for N-parallels of a Landsberg surface.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":"50 1","pages":"165-192"},"PeriodicalIF":0.0,"publicationDate":"2010-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/0023608X-2009-008","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66040389","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quantum continuous $mathfrak{gl}_{infty}$: Semiinfinite construction of representations","authors":"B. Feigin, E. Feigin, M. Jimbo, T. Miwa, E. Mukhin","doi":"10.1215/21562261-1214375","DOIUrl":"https://doi.org/10.1215/21562261-1214375","url":null,"abstract":"We begin a study of the representation theory of quantum continuous $mathfrak{gl}_infty$, which we denote by $mathcal E$. This algebra depends on two parameters and is a deformed version of the enveloping algebra of the Lie algebra of difference operators acting on the space of Laurent polynomials in one variable. Fundamental representations of $mathcal E$ are labeled by a continuous parameter $uin {mathbb C}$. The representation theory of $mathcal E$ has many properties familiar from the representation theory of $mathfrak{gl}_infty$: vector representations, Fock modules, semi-infinite constructions of modules. Using tensor products of vector representations, we construct surjective homomorphisms from $mathcal E$ to spherical double affine Hecke algebras $Sddot H_N$ for all $N$. A key step in this construction is an identification of a natural bases of the tensor products of vector representations with Macdonald polynomials. We also show that one of the Fock representations is isomorphic to the module constructed earlier by means of the $K$-theory of Hilbert schemes.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":"51 1","pages":"337-364"},"PeriodicalIF":0.0,"publicationDate":"2010-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/21562261-1214375","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66024823","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quantum continuous $mathfrak{gl}_{infty}$: Tensor products of Fock modules and $mathcal{W}_{n}$-characters","authors":"B. Feigin, E. Feigin, M. Jimbo, T. Miwa, E. Mukhin","doi":"10.1215/21562261-1214384","DOIUrl":"https://doi.org/10.1215/21562261-1214384","url":null,"abstract":"We construct a family of irreducible representations of the quantum continuous $gl_infty$ whose characters coincide with the characters of representations in the minimal models of the $W_n$ algebras of $gl_n$ type. In particular, we obtain a simple combinatorial model for all representations of the $W_n$-algebras appearing in the minimal models in terms of $n$ interrelating partitions.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":"36 1","pages":"365-392"},"PeriodicalIF":0.0,"publicationDate":"2010-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/21562261-1214384","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66024837","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Gorenstein flat dimension of complexes","authors":"A. Iacob","doi":"10.1215/KJM/1265899484","DOIUrl":"https://doi.org/10.1215/KJM/1265899484","url":null,"abstract":"We define a notion of Gorenstein flat dimension for unbounded complexes over left GF-closed rings. Over Gorenstein rings we introduce a notion of Gorenstein coho- mology for complexes; we also define a generalized Tate cohomol- ogy for complexes over Gorenstein rings, and we show that there is a close connection between the absolute, the Gorenstein and the generalized Tate cohomology.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":"861 1","pages":"817-842"},"PeriodicalIF":0.0,"publicationDate":"2010-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/KJM/1265899484","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66113826","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Fano surface of the Klein cubic threefold","authors":"X. Roulleau","doi":"10.1215/KJM/1248983032","DOIUrl":"https://doi.org/10.1215/KJM/1248983032","url":null,"abstract":"We prove that the Klein cubic threefold $F$ is the only smooth cubic threefold which has an automorphism of order $11$. We compute the period lattice of the intermediate Jacobian of $F$ and study its Fano surface $S$. We compute also the set of fibrations of $S$ onto a curve of positive genus and the intersection between the fibres of these fibrations. These fibres generate an index $2$ sub-group of the Neron-Severi group and we obtain a set of generators of this group. The Neron-Severi group of $S$ has rank $25=h^{1,1}$ and discriminant $11^{10}$.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":"49 1","pages":"113-129"},"PeriodicalIF":0.0,"publicationDate":"2010-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66087227","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the WKB-theoretic structure of a Schrödinger operator with a merging pair of a simple pole and a simple turning point","authors":"S. Kamimoto, T. Kawai, T. Koike, Yoshitsugu Takei","doi":"10.1215/0023608X-2009-007","DOIUrl":"https://doi.org/10.1215/0023608X-2009-007","url":null,"abstract":"A Schrödinger equation with a merging pair of a simple pole and a simple turning point (called MPPT equation for short) is studied from the viewpoint of exact Wentzel-Kramers-Brillouin (WKB) analysis. In a way parallel to the case of mergingturning-points (MTP) equations, we construct a WKB-theoretic transformation that brings anMPPTequation to its canonical form (the ∞-Whittaker equation in this case). Combining this transformation with the explicit description of the Voros coefficient for the Whittaker equation in terms of the Bernoulli numbers found by Koike, we discuss analytic properties of Borel-transformed WKB solutions of an MPPT equation. 0. Introduction The principal aim of this article is to form a basis for the exact WKB analysis of a Schrödinger equation (0.1) ( d dx2 − ηQ(x, η) ) ψ = 0 (η: a large parameter) with one simple turning point and with one simple pole in the potential Q. As [Ko1] and [Ko3] emphasize, the Borel transform of a WKB solution of (0.1) displays, near the simple pole singularity, behavior similar to that near a simple turning point. Hence it is natural to expect that such an equation plays an important role in exact WKB analysis in the large. Such an expectation has recently been enhanced by the discovery (see [KoT]) that the Voros coefficient of a WKB solution of (0.1) with (0.2) Q = 1 4 + α x + η−2 γ x2 (α, γ: fixed complex numbers) can be explicitly written down with the help of the Bernoulli numbers. The potential Q given by (0.2) plays an important role in Section 2; the Schrödinger Kyoto Journal of Mathematics, Vol. 50, No. 1 (2010), 101–164 DOI 10.1215/0023608X-2009-007, © 2010 by Kyoto University Received July 30, 2009. Revised October 2, 2009. Accepted October 9, 2009. Mathematics Subject Classification: Primary 34M60; Secondary 34E20, 34M35, 35A27, 35A30. Authors’ research supported in part by Japan Society for the Promotion of Science Grants-in-Aid 20340028, 21740098, and 21340029. 102 Kamimoto, Kawai, Koike, and Takei equation with the potential Q of the form (0.2), that is, the Whittaker equation with a large parameter η, gives us a WKB-theoretic canonical form of a Schrödinger equation with one simple turning point and with one simple pole in its potential. We note that the parameter α contained in the Whittaker equation in Section 2 is an infinite series α(η) = ∑ k≥0 αkη −k (αk: a constant), and we call such an equation the ∞-Whittaker equation when we want to emphasize that α is not a genuine constant but an infinite series as above. In order to make a semiglobal study of a Schrödinger equation with one simple turning point and with a simple pole in its potential, we let the simple pole singular point merge with the turning point and observe what kind of equation appears. For example, what if we let α tend to zero in (0.2) with γ being kept intact? Interestingly enough, the resulting equation is what we call a ghost equation (see [Ko2]); we have been wondering where we should place the class of g","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":"50 1","pages":"101-164"},"PeriodicalIF":0.0,"publicationDate":"2010-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/0023608X-2009-007","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66040351","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Connes-amenability of multiplier Banach algebras","authors":"B. Hayati, M. Amini","doi":"10.1215/0023608X-2009-003","DOIUrl":"https://doi.org/10.1215/0023608X-2009-003","url":null,"abstract":"Let B be a Banach algebra with bounded approximate identity, and let M(B) be its multiplier algebra. If there exists a continuous linear injection B∗ → M(B) such that, for every b ∈ B and every u, v ∈ B∗, 〈u, vb〉B = 〈v, bu〉B , then M(B) is a dual Banach algebra and the following are equivalent: (i) B is amenable; (ii) M(B) is Connes amenable; (iii) M(B) has a normal, virtual diagonal.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":"50 1","pages":"41-50"},"PeriodicalIF":0.0,"publicationDate":"2010-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/0023608X-2009-003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66040264","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Relation between differential polynomials and small functions","authors":"B. Belaïdi, A. Farissi","doi":"10.1215/0023608X-2009-019","DOIUrl":"https://doi.org/10.1215/0023608X-2009-019","url":null,"abstract":"In this article, we discuss the growth of solutions of the second-order nonhomogeneous linear differential equation where a, b are complex constants and A j ( z ) (cid:2)≡ 0 ( j = 0 , 1) , and F (cid:2)≡ 0 are entire functions such that max { ρ ( A j ) ( j = 0 , 1) ,ρ ( F ) } < 1 . We also investigate the relationship between small functions and differential polynomials g f ( z ) = d 2 f (cid:2)(cid:2) + d 1 f (cid:2) + d 0 f , where d 0 ( z ) ,d 1 ( z ) ,d 2 ( z ) are entire functions that are not all equal to zero with ρ ( d j ) < 1 ( j = 0 , 1 , 2) generated by solutions of the above equation.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":"50 1","pages":"453-468"},"PeriodicalIF":0.0,"publicationDate":"2010-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/0023608X-2009-019","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66040583","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The integral cohomology ring of $E_7/T$","authors":"Masaki Nakagawa","doi":"10.3792/pjaa.86.64","DOIUrl":"https://doi.org/10.3792/pjaa.86.64","url":null,"abstract":"We give a complete description of the integral cohomology ring of the flag manifold E 8 /T, where E 8 denotes the compact exceptional Lie group of rank 8 and T its maximal torus, by the method due to Borel and Toda. This completes the computation of the integral cohomology rings of the flag manifolds for all compact connected simple Lie groups.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":"41 1","pages":"303-321"},"PeriodicalIF":0.0,"publicationDate":"2009-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.3792/pjaa.86.64","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70207733","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On Samelson products in Sp(n)","authors":"Tomoaki Nagao","doi":"10.1215/KJM/1248983038","DOIUrl":"https://doi.org/10.1215/KJM/1248983038","url":null,"abstract":"","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":"49 1","pages":"225-234"},"PeriodicalIF":0.0,"publicationDate":"2009-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66087731","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}