209 citations · 1.2k across the 68 of their papers we have counts for
18 papers · 1 filter
Hall-Littlewood-positive harmonic functionals on the algebra of symmetric functions
Cesar Cuenca, Grigori Olshanski
We study the problem of describing the set of real functionals on the quotient of the ring of symmetric functions that are nonnegative on the images of certa…
Elements of the q-Askey scheme in the algebra of symmetric functions
Cesar Cuenca, Grigori Olshanski
The classical q-hypergeometric orthogonal polynomials are assembled into a hierarchy called the q-Askey scheme. At the top of the hierarchy, there are two closely related families,…
Interpolation Macdonald polynomials and Cauchy-type identities
Grigori Olshanski
Let Sym denote the algebra of symmetric functions and and be the Macdonald symmetric functions (recall that they differ by scalar factors…
An analogue of big q-Jacobi polynomials in the algebra of symmetric functions
Grigori Olshanski
The main result of the paper is a construction of a five-parameter family of new bases in the algebra of symmetric functions. These bases are inhomogeneous and share many propertie…
The Gelfand-Tsetlin graph and Markov processes
Grigori Olshanski
The goal of the paper is to describe new connections between representation theory and algebraic combinatorics on one side, and probability theory on the other side. The central re…
The boundary of the Gelfand-Tsetlin graph: A new approach
Alexei Borodin, Grigori Olshanski
The Gelfand-Tsetlin graph is an infinite graded graph that encodes branching of irreducible characters of the unitary groups. The boundary of the Gelfand-Tsetlin graph has at least…