2022/10/23 by D. V. Artamonov, Artamonov, D. V. · 1 citation
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Complex Variables (math.CV) #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2210.12680
openalex publication_date 2022/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
In the paper we consider a realization of a finite dimensional irreducible representation of the Lie algebra \mathfrakgln in the space of functions on the group GLn. It is proved that functions corresponding to Gelfand-Tsetlin diagrams are linear combinations of some new functions of hypergeometric type which are closely related to A-hypergeometric functions. These new functions are solution of a system of partial differential equations which one obtains from the Gelfand-Kapranov-Zelevinsky by an "antisymmetrization". The coefficients in the constructed linear combination are hypergeometric constants i.e. they are values of some hypergeometric functions when instead of all arguments ones are substituted.