Seminar 15.10.2025: Dmitry Artamonov (MSU)

Title: Functional realization of the Gelfand-Tselin base Abstract: Consider a realization of finite-dimensional irreducible representations of gl(n) in the space of functions on the group GL(n). The question is: which functions on the group correspond to the Gelfand-Tsetlin basis vectors? The answer has been known since the 1960s for the first non-trivial case, n=3. In this case, the corresponding functions are written as the result of a substitution of a certain expression involving determinants on the group into the Gauss hypergeometric function. In the talk a generalization of this result to the case of arbitrary n will be presented. To obtain such a generalization certain classes of functions and systems of hypergeometric type (close to GKZ functions) will be constructed.