Nagoya Mathematical Journal最新文献_第8页

EXTENSIONS OF CHARACTERS IN TYPE D AND THE INDUCTIVE MCKAY CONDITION, I 类型d中字符的扩展和归纳McKay条件

IF 0.8 2区数学

Nagoya Mathematical Journal Pub Date : 2021-09-16 DOI: 10.1017/nmj.2023.14

Britta Späth

{"title":"EXTENSIONS OF CHARACTERS IN TYPE D AND THE INDUCTIVE MCKAY CONDITION, I","authors":"Britta Späth","doi":"10.1017/nmj.2023.14","DOIUrl":"https://doi.org/10.1017/nmj.2023.14","url":null,"abstract":"\u0000 This is a contribution to the study of \u0000 \u0000 \u0000 \u0000$mathrm {Irr}(G)$\u0000\u0000 \u0000 as an \u0000 \u0000 \u0000 \u0000$mathrm {Aut}(G)$\u0000\u0000 \u0000 -set for G a finite quasisimple group. Focusing on the last open case of groups of Lie type \u0000 \u0000 \u0000 \u0000$mathrm {D}$\u0000\u0000 \u0000 and \u0000 \u0000 \u0000 \u0000$^2mathrm {D}$\u0000\u0000 \u0000 , a crucial property is the so-called \u0000 \u0000 \u0000 \u0000$A'(infty )$\u0000\u0000 \u0000 condition expressing that diagonal automorphisms and graph-field automorphisms of G have transversal orbits in \u0000 \u0000 \u0000 \u0000$mathrm {Irr}(G)$\u0000\u0000 \u0000 . This is part of the stronger \u0000 \u0000 \u0000 \u0000$A(infty )$\u0000\u0000 \u0000 condition introduced in the context of the reduction of the McKay conjecture to a question about quasisimple groups. Our main theorem is that a minimal counterexample to condition \u0000 \u0000 \u0000 \u0000$A(infty )$\u0000\u0000 \u0000 for groups of type \u0000 \u0000 \u0000 \u0000$mathrm {D}$\u0000\u0000 \u0000 would still satisfy \u0000 \u0000 \u0000 \u0000$A'(infty )$\u0000\u0000 \u0000 . This will be used in a second paper to fully establish \u0000 \u0000 \u0000 \u0000$A(infty )$\u0000\u0000 \u0000 for any type and rank. The present paper uses Harish-Chandra induction as a parametrization tool. We give a new, more effective proof of the theorem of Geck and Lusztig ensuring that cuspidal characters of any standard Levi subgroup of \u0000 \u0000 \u0000 \u0000$G=mathrm {D}_{ l,mathrm {sc}}(q)$\u0000\u0000 \u0000 extend to their stabilizers in the normalizer of that Levi subgroup. This allows us to control the action of automorphisms on these extensions. From there, Harish-Chandra theory leads naturally to a detailed study of associated relative Weyl groups and other extendibility problems in that context.","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47130810","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 11

A REALIZATION OF THE ENVELOPING SUPERALGEBRA $ {mathcal U}_{mathbb Q}(widehat {mathfrak {gl}}_{m|n})$ 包络超代数$ {mathcal U}_{mathbb Q}(widehat {mathfrak {gl}}_{m|n})$的实现

IF 0.8 2区数学

Nagoya Mathematical Journal Pub Date : 2021-09-09 DOI: 10.1017/nmj.2021.11

J. Du, Qiang Fu, Yanan Lin

{"title":"A REALIZATION OF THE ENVELOPING SUPERALGEBRA \u0000$ {mathcal U}_{mathbb Q}(widehat {mathfrak {gl}}_{m|n})$","authors":"J. Du, Qiang Fu, Yanan Lin","doi":"10.1017/nmj.2021.11","DOIUrl":"https://doi.org/10.1017/nmj.2021.11","url":null,"abstract":"Abstract In [2], Beilinson–Lusztig–MacPherson (BLM) gave a beautiful realization for quantum \u0000$mathfrak {gl}_n$\u0000 via a geometric setting of quantum Schur algebras. We introduce the notion of affine Schur superalgebras and use them as a bridge to link the structure and representations of the universal enveloping superalgebra \u0000${mathcal U}_{mathbb Q}(widehat {mathfrak {gl}}_{m|n})$\u0000 of the loop algebra \u0000$widehat {mathfrak {gl}}_{m|n}$\u0000 of \u0000${mathfrak {gl}}_{m|n}$\u0000 with those of affine symmetric groups \u0000${widehat {{mathfrak S}}_{r}}$\u0000 . Then, we give a BLM type realization of \u0000${mathcal U}_{mathbb Q}(widehat {mathfrak {gl}}_{m|n})$\u0000 via affine Schur superalgebras. The first application of the realization of \u0000${mathcal U}_{mathbb Q}(widehat {mathfrak {gl}}_{m|n})$\u0000 is to determine the action of \u0000${mathcal U}_{mathbb Q}(widehat {mathfrak {gl}}_{m|n})$\u0000 on tensor spaces of the natural representation of \u0000$widehat {mathfrak {gl}}_{m|n}$\u0000 . These results in epimorphisms from \u0000$;{mathcal U}_{mathbb Q}(widehat {mathfrak {gl}}_{m|n})$\u0000 to affine Schur superalgebras so that the bridging relation between representations of \u0000${mathcal U}_{mathbb Q}(widehat {mathfrak {gl}}_{m|n})$\u0000 and \u0000${widehat {{mathfrak S}}_{r}}$\u0000 is established. As a second application, we construct a Kostant type \u0000$mathbb Z$\u0000 -form for \u0000${mathcal U}_{mathbb Q}(widehat {mathfrak {gl}}_{m|n})$\u0000 whose images under the epimorphisms above are exactly the integral affine Schur superalgebras. In this way, we obtain essentially the super affine Schur–Weyl duality in arbitrary characteristics.","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":"247 1","pages":"516 - 551"},"PeriodicalIF":0.8,"publicationDate":"2021-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48552706","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

GENERALIZED GREEN FUNCTIONS AND UNIPOTENT CLASSES FOR FINITE REDUCTIVE GROUPS, III 有限归约群的广义格林函数和单能类

IF 0.8 2区数学

Nagoya Mathematical Journal Pub Date : 2021-09-03 DOI: 10.1017/nmj.2021.12

T. Shoji

引用次数: 2

NMJ volume 243 Cover and Front matter NMJ第243卷封面和封面问题

IF 0.8 2区数学

Nagoya Mathematical Journal Pub Date : 2021-09-01 DOI: 10.1017/s0027763020000252

引用次数: 0

NMJ volume 243 Cover and Back matter NMJ第243卷封面和封底

IF 0.8 2区数学

Nagoya Mathematical Journal Pub Date : 2021-09-01 DOI: 10.1017/s0027763020000264

引用次数: 0

ENERGY CONCENTRATION PROPERTIES OF A p-GINZBURG–LANDAU MODEL p-GINZBURG-LANDAU模型的能量集中性质

IF 0.8 2区数学

Nagoya Mathematical Journal Pub Date : 2021-08-25 DOI: 10.1017/nmj.2021.10

Y. Lei

引用次数: 0

ON THE MILNOR FIBRATION OF CERTAIN NEWTON DEGENERATE FUNCTIONS 关于某些牛顿退化函数的MILNOR FIBRATION

IF 0.8 2区数学

Nagoya Mathematical Journal Pub Date : 2021-08-18 DOI: 10.1017/nmj.2022.37

C. Eyral, M. Oka

引用次数: 0

LIE ALGEBRA MODULES WHICH ARE LOCALLY FINITE AND WITH FINITE MULTIPLICITIES OVER THE SEMISIMPLE PART 局部有限且在半单部分上具有有限复数的李代数模

IF 0.8 2区数学

Nagoya Mathematical Journal Pub Date : 2021-08-02 DOI: 10.1017/nmj.2021.8

V. Mazorchuk, Rafael Mrðen

{"title":"LIE ALGEBRA MODULES WHICH ARE LOCALLY FINITE AND WITH FINITE MULTIPLICITIES OVER THE SEMISIMPLE PART","authors":"V. Mazorchuk, Rafael Mrðen","doi":"10.1017/nmj.2021.8","DOIUrl":"https://doi.org/10.1017/nmj.2021.8","url":null,"abstract":"Abstract For a finite-dimensional Lie algebra \u0000$mathfrak {L}$\u0000 over \u0000$mathbb {C}$\u0000 with a fixed Levi decomposition \u0000$mathfrak {L} = mathfrak {g} ltimes mathfrak {r}$\u0000 , where \u0000$mathfrak {g}$\u0000 is semisimple, we investigate \u0000$mathfrak {L}$\u0000 -modules which decompose, as \u0000$mathfrak {g}$\u0000 -modules, into a direct sum of simple finite-dimensional \u0000$mathfrak {g}$\u0000 -modules with finite multiplicities. We call such modules \u0000$mathfrak {g}$\u0000 -Harish-Chandra modules. We give a complete classification of simple \u0000$mathfrak {g}$\u0000 -Harish-Chandra modules for the Takiff Lie algebra associated to \u0000$mathfrak {g} = mathfrak {sl}_2$\u0000 , and for the Schrödinger Lie algebra, and obtain some partial results in other cases. An adapted version of Enright’s and Arkhipov’s completion functors plays a crucial role in our arguments. Moreover, we calculate the first extension groups of infinite-dimensional simple \u0000$mathfrak {g}$\u0000 -Harish-Chandra modules and their annihilators in the universal enveloping algebra, for the Takiff \u0000$mathfrak {sl}_2$\u0000 and the Schrödinger Lie algebra. In the general case, we give a sufficient condition for the existence of infinite-dimensional simple \u0000$mathfrak {g}$\u0000 -Harish-Chandra modules.","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":"41 1","pages":"430 - 470"},"PeriodicalIF":0.8,"publicationDate":"2021-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87837443","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

IWASAWA THEORY FOR p-TORSION CLASS GROUP SCHEMES IN CHARACTERISTIC p 特征p-扭转类群方案的IWASAWA理论

IF 0.8 2区数学

Nagoya Mathematical Journal Pub Date : 2021-07-27 DOI: 10.1017/nmj.2022.30

J. Booher, Bryden Cais

{"title":"IWASAWA THEORY FOR p-TORSION CLASS GROUP SCHEMES IN CHARACTERISTIC p","authors":"J. Booher, Bryden Cais","doi":"10.1017/nmj.2022.30","DOIUrl":"https://doi.org/10.1017/nmj.2022.30","url":null,"abstract":"Abstract We investigate a novel geometric Iwasawa theory for \u0000${mathbf Z}_p$\u0000 -extensions of function fields over a perfect field k of characteristic \u0000$p>0$\u0000 by replacing the usual study of p-torsion in class groups with the study of p-torsion class group schemes. That is, if \u0000$cdots to X_2 to X_1 to X_0$\u0000 is the tower of curves over k associated with a \u0000${mathbf Z}_p$\u0000 -extension of function fields totally ramified over a finite nonempty set of places, we investigate the growth of the p-torsion group scheme in the Jacobian of \u0000$X_n$\u0000 as \u0000$nrightarrow infty $\u0000 . By Dieudonné theory, this amounts to studying the first de Rham cohomology groups of \u0000$X_n$\u0000 equipped with natural actions of Frobenius and of the Cartier operator V. We formulate and test a number of conjectures which predict striking regularity in the \u0000$k[V]$\u0000 -module structure of the space \u0000$M_n:=H^0(X_n, Omega ^1_{X_n/k})$\u0000 of global regular differential forms as \u0000$nrightarrow infty .$\u0000 For example, for each tower in a basic class of \u0000${mathbf Z}_p$\u0000 -towers, we conjecture that the dimension of the kernel of \u0000$V^r$\u0000 on \u0000$M_n$\u0000 is given by \u0000$a_r p^{2n} + lambda _r n + c_r(n)$\u0000 for all n sufficiently large, where \u0000$a_r, lambda _r$\u0000 are rational constants and \u0000$c_r : {mathbf Z}/m_r {mathbf Z} to {mathbf Q}$\u0000 is a periodic function, depending on r and the tower. To provide evidence for these conjectures, we collect extensive experimental data based on new and more efficient algorithms for working with differentials on \u0000${mathbf Z}_p$\u0000 -towers of curves, and we prove our conjectures in the case \u0000$p=2$\u0000 and \u0000$r=1$\u0000 .","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":"250 1","pages":"298 - 351"},"PeriodicalIF":0.8,"publicationDate":"2021-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43187510","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

POSITIVELY CURVED FINSLER METRICS ON VECTOR BUNDLES 向量束上的正弯曲finsler度量

IF 0.8 2区数学

Nagoya Mathematical Journal Pub Date : 2021-07-01 DOI: 10.1017/nmj.2022.2

Kuang-Ru Wu

引用次数: 1