Identities from representation theory
- 주제(키워드) Catalan number , Jacobi–Trudi formula , q-analog
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- OA유형 Green Submitted
- 발행기관 Elsevier B.V.
- 발행년도 2019
- URI http://www.dcollection.net/handler/ewha/000000160763
- 본문언어 영어
- Published As http://dx.doi.org/10.1016/j.disc.2019.05.020
초록/요약
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.
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