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Identities from representation theory

Title
Identities from representation theory
Authors
Oh S.-J.Scrimshaw T.
Ewha Authors
오세진
SCOPUS Author ID
오세진scopus
Issue Date
2019
Journal Title
Discrete Mathematics
ISSN
0012-365XJCR Link
Citation
Discrete Mathematics vol. 342, no. 9, pp. 2493 - 2541
Keywords
Catalan numberJacobi–Trudi formulaq-analog
Publisher
Elsevier B.V.
Indexed
SCI; SCIE; SCOPUS WOS scopus
Document Type
Article
Abstract
We give a new Jacobi–Trudi-type formula for characters of finite-dimensional irreducible representations in type Cn using characters of the fundamental representations and non-intersecting lattice paths. We give equivalent determinant formulas for the decomposition multiplicities for tensor powers of the spin representation in type Bn and the exterior representation in type Cn. This gives a combinatorial proof of an identity of Katz and equates such a multiplicity with the dimension of an irreducible representation in type Cn. By taking certain specializations, we obtain identities for q-Catalan triangle numbers, a slight modification of the q,t-Catalan number of Stump, q-triangle versions of Motzkin and Riordan numbers, and generalizations of Touchard's identity. We use (spin) rigid tableaux and crystal base theory to show some formulas relating Catalan, Motzkin, and Riordan triangle numbers. © 2019 Elsevier B.V.
DOI
10.1016/j.disc.2019.05.020
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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