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引用次数: 0
摘要
我们证明了一个新的正辛李超代数不可约表示性质的行列式，类似于Moens和Jeugt （J代数组合17(3):283 - 307,2003）的一般线性李超代数的行列式。我们的证明使用Jacobi-Trudi型公式来证明正辛特征。因此，我们证明了由Proctor （Invent Math 92(2): 307-332, 1988）引入的奇辛字符与具有某些特殊不定数的正辛字符相同。我们还对Brent， Krattenthaler和Warnaar的奇辛特征恒等式进行了推广（J组合理论学报，144:80-138,2016）。
A Determinantal Formula for Orthosymplectic Schur Functions
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
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