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A note on weight systems which are quantum states 关于量子态的权重系统的注释
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-10-11 DOI: 10.4153/s0008439523000206
Carlo Collari
{"title":"A note on weight systems which are quantum states","authors":"Carlo Collari","doi":"10.4153/s0008439523000206","DOIUrl":"https://doi.org/10.4153/s0008439523000206","url":null,"abstract":"A result of Corfield, Sati, and Schreiber asserts that $mathfrak{gl}_n$-weight systems associated to the defining representation are quantum states. In this short note we extend this result to all $mathfrak{gl}_n$-weight systems corresponding to labeling by symmetric and exterior powers of the defining representation.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48425175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 2
Benford behavior and distribution in residue classes of large prime factors 大素数因子残馀类中的Benford行为与分布
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-10-10 DOI: 10.4153/S0008439522000601
P. Pollack, Akash Singha Roy
{"title":"Benford behavior and distribution in residue classes of large prime factors","authors":"P. Pollack, Akash Singha Roy","doi":"10.4153/S0008439522000601","DOIUrl":"https://doi.org/10.4153/S0008439522000601","url":null,"abstract":"Abstract We investigate the leading digit distribution of the kth largest prime factor of n (for each fixed \u0000$k=1,2,3,dots $\u0000 ) as well as the sum of all prime factors of n. In each case, we find that the leading digits are distributed according to Benford’s law. Moreover, Benford behavior emerges simultaneously with equidistribution in arithmetic progressions uniformly to small moduli.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43181377","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Compatibility of theta lifts and tempered condition 升力和回火条件的兼容性
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-09-22 DOI: 10.4153/s0008439523000516
Zhe Li, Shanwen Wang
{"title":"Compatibility of theta lifts and tempered condition","authors":"Zhe Li, Shanwen Wang","doi":"10.4153/s0008439523000516","DOIUrl":"https://doi.org/10.4153/s0008439523000516","url":null,"abstract":"\u0000 In this note, assuming the nonvanishing result of explicit theta correspondence for the symplectic–orthogonal dual pair over quaternion algebra \u0000 \u0000 \u0000 \u0000$mathbb {H}$\u0000\u0000 \u0000 , we show that, for metapletic–orthogonal dual pair over \u0000 \u0000 \u0000 \u0000$mathbb {R}$\u0000\u0000 \u0000 and the symplectic–orthogonal dual pair over quaternion algebra \u0000 \u0000 \u0000 \u0000$mathbb {H}$\u0000\u0000 \u0000 , the theta correspondence is compatible with tempered condition by directly estimating the matrix coefficients, without using the classification theorem.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45492197","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Characterizing slopes for the $(-2,3,7)$ -pretzel knot 描述$（-2,3,7）$椒盐卷饼结的斜率
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-09-21 DOI: 10.4153/S0008439523000073
D. McCoy
{"title":"Characterizing slopes for the \u0000$(-2,3,7)$\u0000 -pretzel knot","authors":"D. McCoy","doi":"10.4153/S0008439523000073","DOIUrl":"https://doi.org/10.4153/S0008439523000073","url":null,"abstract":"Abstract In this note, we exhibit concrete examples of characterizing slopes for the knot \u0000$12n242$\u0000 , also known as the \u0000$(-2,3,7)$\u0000 -pretzel knot. Although it was shown by Lackenby that every knot admits infinitely many characterizing slopes, the nonconstructive nature of the proof means that there are very few hyperbolic knots for which explicit examples of characterizing slopes are known.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46972539","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Families of Young Functions and Limits of Orlicz Norms Young函数族与Orlicz范数极限
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-09-02 DOI: 10.4153/s0008439523000449
S. Rodney, S. F. MacDonald
{"title":"Families of Young Functions and Limits of Orlicz Norms","authors":"S. Rodney, S. F. MacDonald","doi":"10.4153/s0008439523000449","DOIUrl":"https://doi.org/10.4153/s0008439523000449","url":null,"abstract":"Given a $sigma$-finite measure space $(X,mu)$, a Young function $Phi$, and a one-parameter family of Young functions ${Psi_q}$, we find necessary and sufficient conditions for the associated Orlicz norms of any function $fin L^Phi(X,mu)$ to satisfy [ lim_{qrightarrow infty}|f|_{L^{Psi_q}(X,mu)}=C|f|_{L^infty(X,mu)}. ] The constant $C$ is independent of $f$ and depends only on the family ${Psi_q}$. Several examples of one-parameter families of Young functions satisfying our conditions are given, along with counterexamples when our conditions fail.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42500604","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
BCM volume 65 issue 3 Cover and Back matter BCM第65卷第3期封面和封底
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-08-25 DOI: 10.4153/s0008439522000455
{"title":"BCM volume 65 issue 3 Cover and Back matter","authors":"","doi":"10.4153/s0008439522000455","DOIUrl":"https://doi.org/10.4153/s0008439522000455","url":null,"abstract":"","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48856852","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
BCM volume 65 issue 3 Cover and Front matter BCM第65卷第3期封面和封面
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-08-25 DOI: 10.4153/s0008439522000467
{"title":"BCM volume 65 issue 3 Cover and Front matter","authors":"","doi":"10.4153/s0008439522000467","DOIUrl":"https://doi.org/10.4153/s0008439522000467","url":null,"abstract":"","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49465656","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
TORIC DEGENERATIONS OF LOW DEGREE HYPERSURFACES 低阶超曲面的复曲面退化
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-08-24 DOI: 10.4153/s0008439523000309
N. Ilten, Oscar Lautsch
{"title":"TORIC DEGENERATIONS OF LOW DEGREE HYPERSURFACES","authors":"N. Ilten, Oscar Lautsch","doi":"10.4153/s0008439523000309","DOIUrl":"https://doi.org/10.4153/s0008439523000309","url":null,"abstract":"Abstract We show that a sufficiently general hypersurface of degree d in \u0000$mathbb {P}^n$\u0000 admits a toric Gröbner degeneration after linear change of coordinates if and only if \u0000$dleq 2n-1$\u0000 .","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46603486","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
A note on the relative growth of products of multiple partial quotients in the plane 平面上多个偏商乘积的相对增长问题
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-08-19 DOI: 10.4153/S0008439522000510
Adam Brown-Sarre, Mumtaz Hussain
{"title":"A note on the relative growth of products of multiple partial quotients in the plane","authors":"Adam Brown-Sarre, Mumtaz Hussain","doi":"10.4153/S0008439522000510","DOIUrl":"https://doi.org/10.4153/S0008439522000510","url":null,"abstract":"Abstract Let \u0000$r=[a_1(r), a_2(r),ldots ]$\u0000 be the continued fraction expansion of a real number \u0000$rin mathbb R$\u0000 . The growth properties of the products of consecutive partial quotients are tied up with the set admitting improvements to Dirichlet’s theorem. Let \u0000$(t_1, ldots , t_m)in mathbb R_+^m$\u0000 , and let \u0000$Psi :mathbb {N}rightarrow (1,infty )$\u0000 be a function such that \u0000$Psi (n)to infty $\u0000 as \u0000$nto infty $\u0000 . We calculate the Hausdorff dimension of the set of all \u0000$ (x, y)in [0,1)^2$\u0000 such that \u0000$$ begin{align*} maxleft{prod_{i=1}^ma_{n+i}^{t_i}(x), prod_{i=1}^ma_{n+i}^{t_i}(y)right} geq Psi(n) end{align*} $$\u0000 is satisfied for all \u0000$ngeq 1$\u0000 .","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47148957","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
A parametrization of sheets of conjugacy classes in bad characteristic 具有不良特征的共轭类片的参数化
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-08-17 DOI: 10.4153/S0008439523000097
F. Ambrosio, G. Carnovale, F. Esposito
{"title":"A parametrization of sheets of conjugacy classes in bad characteristic","authors":"F. Ambrosio, G. Carnovale, F. Esposito","doi":"10.4153/S0008439523000097","DOIUrl":"https://doi.org/10.4153/S0008439523000097","url":null,"abstract":"Abstract Let G be a simple algebraic group of adjoint type over an algebraically closed field k of bad characteristic. We show that its sheets of conjugacy classes are parametrized by G-conjugacy classes of pairs \u0000$(M,{mathcal O})$\u0000 where M is the identity component of the centralizer of a semisimple element in G and \u0000${mathcal O}$\u0000 is a rigid unipotent conjugacy class in M, in analogy with the good characteristic case.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46194631","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
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