209 citations · 1.2k across the 68 of their papers we have counts for
23 papers · 1 filter
Limits of group algebras for growing symmetric groups and wreath products
Irina Devyatkova, Grigori Olshanski
Let denote the infinite symmetric group formed by the finitary permutations of the set of natural numbers; this is a countable group. We introduce its virtual group alg…
Remarks on Yangian-type algebras and double Poisson brackets
Grigori Olshanski, Nikita Safonkin
This short note is an announcement of results. We continue the study of Yangian-type algebras initiated in the paper arXiv:2208.04809. These algebras share a number of properties o…
The centralizer construction and Yangian-type algebras
Grigori Olshanski
Let be a positive integer. The Yangian of the general linear Lie algebra has countably many generators and quad…
Mackey-type identity for invariant functions on Lie algebras of finite unitary groups and an application
Cesar Cuenca, Grigori Olshanski
The Mackey-type identity mentioned in the title relates the operations of parabolic induction and restriction for invariant functions on the Lie algebras of the finite unitary grou…
Infinite-dimensional groups over finite fields and Hall-Littlewood symmetric functions
Cesar Cuenca, Grigori Olshanski
The groups mentioned in the title are certain matrix groups of infinite size over a finite field . They are built from finite classical groups and at the same time the…
A quantization of the harmonic analysis on the infinite-dimensional unitary group
Vadim Gorin, Grigori Olshanski
The present work stemmed from the study of the problem of harmonic analysis on the infinite-dimensional unitary group U(\infty). That problem consisted in the decomposition of a ce…