{"title":"A Determinantal Formula for Orthosymplectic Schur Functions","authors":"Nishu Kumari","doi":"10.1007/s00026-024-00718-x","DOIUrl":null,"url":null,"abstract":"<div><p>We prove a new determinantal formula for the characters of irreducible representations of orthosymplectic Lie superalgebras analogous to the formula developed by Moens and Jeugt (J Algebraic Combin 17(3):283–307, 2003) for general linear Lie superalgebras. Our proof uses the Jacobi–Trudi type formulas for orthosymplectic characters. As a consequence, we show that the odd symplectic characters introduced by Proctor (Invent Math 92(2):307–332, 1988) are the same as the orthosymplectic characters with some specialized indeterminates. We also give a generalization of an odd symplectic character identity due to Brent, Krattenthaler and Warnaar (J Combin Theory Ser A 144:80–138, 2016).</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"29 3","pages":"719 - 741"},"PeriodicalIF":0.7000,"publicationDate":"2024-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Combinatorics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00026-024-00718-x","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
We prove a new determinantal formula for the characters of irreducible representations of orthosymplectic Lie superalgebras analogous to the formula developed by Moens and Jeugt (J Algebraic Combin 17(3):283–307, 2003) for general linear Lie superalgebras. Our proof uses the Jacobi–Trudi type formulas for orthosymplectic characters. As a consequence, we show that the odd symplectic characters introduced by Proctor (Invent Math 92(2):307–332, 1988) are the same as the orthosymplectic characters with some specialized indeterminates. We also give a generalization of an odd symplectic character identity due to Brent, Krattenthaler and Warnaar (J Combin Theory Ser A 144:80–138, 2016).
期刊介绍：
Annals of Combinatorics publishes outstanding contributions to combinatorics with a particular focus on algebraic and analytic combinatorics, as well as the areas of graph and matroid theory. Special regard will be given to new developments and topics of current interest to the community represented by our editorial board.
The scope of Annals of Combinatorics is covered by the following three tracks:
Algebraic Combinatorics:
Enumerative combinatorics, symmetric functions, Schubert calculus / Combinatorial Hopf algebras, cluster algebras, Lie algebras, root systems, Coxeter groups / Discrete geometry, tropical geometry / Discrete dynamical systems / Posets and lattices
Analytic and Algorithmic Combinatorics:
Asymptotic analysis of counting sequences / Bijective combinatorics / Univariate and multivariable singularity analysis / Combinatorics and differential equations / Resolution of hard combinatorial problems by making essential use of computers / Advanced methods for evaluating counting sequences or combinatorial constants / Complexity and decidability aspects of combinatorial sequences / Combinatorial aspects of the analysis of algorithms
Graphs and Matroids:
Structural graph theory, graph minors, graph sparsity, decompositions and colorings / Planar graphs and topological graph theory, geometric representations of graphs / Directed graphs, posets / Metric graph theory / Spectral and algebraic graph theory / Random graphs, extremal graph theory / Matroids, oriented matroids, matroid minors / Algorithmic approaches
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
