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Shifted Schur functions II. Binomial formula for characters of classical groups and applications
Andrei Okounkov, Grigori Olshanski
Let G be any of the complex classical groups GL(n), SO(2n+1), Sp(2n), O(2n), let g denote the Lie algebra of G, and let Z(g) denote the subalgebra of G-invariants in the universal…
Shifted Jack polynomials, binomial formula, and applications
Andrei Okounkov, Grigori Olshanski
In this note we prove an explicit binomial formula for Jack polynomials and discuss some applications of it.
Shifted Schur Functions
Andrei Okounkov, Grigori Olshanski
The classical algebra of symmetric functions has a remarkable deformation , which we call the algebra of shifted symmetric functions. In the latter algebra, there is a dis…
Ergodic unitarily invariant measures on the space of infinite Hermitian matrices
Grigori Olshanski, Anatoli Vershik
Let be the space of all Hermitian matrices of infinite order and be the inductive limit of the chain of compact unitary groups. The gro…