A relationship between Gelfand-Tsetlin bases and Chari-Loktev bases for irreducible finite dimensional representations of special linear Lie algebras

2019/03/07 by K. N. Raghavan, Raghavan, K N, B. Ravinder +3
Mathematics · Physics and Astronomy · #17B10 (05E10) #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1903.02768

openalex publication_date 2019/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider two bases for an arbitrary finite dimensional irreducible representation of a complex special linear Lie algebra: the classical Gelfand-Tsetlin basis and the relatively new Chari-Loktev basis. Both are parametrized by the set of (integral Gelfand-Tsetlin) patterns with a fixed bounding sequence determined by the highest weight of the representation. We define the "row-wise dominance" partial order on this set of patterns, and prove that the transition matrix between the two bases is triangular with respect to this partial order. We write down explicit expressions for the diagonal elements of the transition matrix.

Citations

• On Chari-Loktev bases for local Weyl modules in type A

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