Speaker: Gurevich Dimitry (IITP, Moscow)
Date and time:  24.05.2023, 17:00 (GMT +03:00)
Title:  Reflection Equation Algebra and related combinatorics

Abstract: Reflection Equation Algebras constitute a subclass of the so-called  Quantum Matrix algebras. Each of the REA is associated with a quantum $R$-matrix. In a sense the REA corresponding to quantum R-matrix of Hecke type can be considered as q-counterparts of the commutative algebra Sym(gl(N)) or the enveloping algebras U(gl(N)) depending on its realization. On any such RE algebra there exist analogs of some symmetric polynomials, namely  the power sums and the Schur functions.

In my talk I plan to exhibit q-versions  of the Capelli formula, the Frobenius formula, related to  this combinatorics. Also I plan to introduce analogs of the Casimir operators and  perform  their spectral analysis.

To access the online seminar please contact  Anna Tolbey bekvaanna@gmail.com