Asymptotic representation theory lectures by G. Olshanski (in Russian)
- Fall 2009
- Characters of the infinite-dimensional unitary group
- Shifted symmetric functions
- Total nonnegativity
- Factor representations of infinite-dimensional unitary group
- Point processes related to the unitary groups
- Spring 2010
- Schur-Weyl duality
- Robinson-Schensted correspondence
- Plancherel measures, difference operators
- Orbital HCIZ integrals
- Classification of ergodic central measures on infinite-dimensional Hermitian matrices
sl(2) Operators and Markov Processes on Branching Graphs
We present a unified approach to various examples of Markov dynamics on partitions studied by Borodin, Olshanski, Fulman, and the author. Our technique generalizes the Kerov’s operators first appeared in [Okounkov, arXiv:math/0002135], and also stems from the study of duality of graded graphs in [Fomin, 1994].
sl(2) Operators and Markov Dynamics on Branching Graphs
The talk is based on [8] and describes $\mathfrak{sl}(2,\mathbb{C})$ structures behind Markov jump processes on the Young and related branching graphs
MATH 1342 • Calculus II for Sci&Eng
On Measures on Partitions Arising in Harmonic Analysis for Linear and Projective Characters of the Infinite Symmetric Group
The z-measures on partitions originated from the problem of harmonic analysis of linear representations of the infinite symmetric group in the works of Kerov, Olshanski and Vershik (1993, 2004). A similar family corresponding to projective representations was introduced by Borodin (1997). The latter measures live on strict partitions (i.e., partitions with distinct parts), and the z-measures are supported by all partitions. In this note we describe some combinatorial relations between these two families of measures using the well-known doubling of shifted Young diagrams.
Combinatorics
Course taught in English at the Math in Moscow programme for international undergraduate students at the Independent University of Moscow, Spring 2011.
Pfaffian Stochastic Dynamics of Strict Partitions
We study a family of continuous time Markov jump processes on strict partitions (partitions with distinct parts) preserving the distributions introduced by Borodin (1997) in connection with projective representations of the infinite symmetric group.
Random Strict Partitions and Determinantal Point Processes
In this note we present new examples of determinantal point processes with infinitely many particles.