Relative Weyl Character formula, Relative Pieri formulas and Branching rules for Classical groups

Autor:	Rajan, C. S., Shrivastava, Sagar
Rok vydání:	2023
Předmět:	Mathematics - Representation Theory 17B45 20G05 20G20 11E57
Druh dokumentu:	Working Paper
Popis:	We give alternate proofs of the classical branching rules for highest weight representations of a complex reductive group $G$ restricted to a closed regular reductive subgroup $H$, where $(G,H)$ consist of the pairs $(GL(n+1),GL(n))$, $ (Spin(2n+1), Spin(2n)) $ and $(Sp(2n),Sp(2)\times Sp(2n-2))$. Our proof is essentially a long division. The starting point is a relative Weyl character formula and our method is an inductive application of a relative Pieri formula. We also give a proof of the branching rule for the case of $ (Spin(2n), Spin(2n-1))$, by a reduction to the case of $(GL(n),GL(n-1))$. Comment: 35 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2310.00323 Zobrazit plný text záznamu View this record from Arxiv