We will discuss the classical problem of describing analogues of irreducible representations of the infinite-dimensional unitary group (Edrei-Voiculescu theorem), and its connections with
The schedule is subject to change as we progress with the topics.
January 18, 2019, special location - Ruffner Hall 127.
Leo Petrov - Introduction “The many facets of the Edrei-Voiculescu theorem”
January 25, 2019, special location - Ruffner Hall 123.
Liron Speyer - $U(N)$: weights, irreducible characters, Schur polynomials, branching
[standard textbooks like the H. Weyl’s], a summary is in [section 2.2 in arXiv:1310.8007]
February 1, 2019
George Seelinger - Extreme characters of $U(\infty)$: definition and two elementary examples [PDF notes]
[for example, section 4.1.10 in these draft lecture notes]
February 8, 2019
Axel Saenz - Functional equation for irreducible characters and the ring theorem for extreme characters of $U(\infty)$
[G. Olshanski, On semigroups related to infinite-dimensional groups. In: Topics in Representation Theory (A. A. Kirillov, ed.). Advances in Soviet Math.] or [A. Borodin, G. Olsahnski “Representations of the Infinite Symmetric Group”, exercises 1.5 and 4.3]
February 15, 2019
Ethan Zell - Projection formula for Gibbs measures on tilings (formula for the number of trapezoidal Gelfand-Tsetlin schemes)
[arXiv:1109.1412 and arXiv:1208.3443]
February 22, 2019
Leo Petrov - Idea of proof of Edrei-Voiculescu theorem
[arXiv:1109.1412]
March 1, 2019
No meeting
March 8, 2019
Joseph Eisner - Characters and von Neumman factor representations. GNS construction
March 22, 2019
Axel Saenz - Pascal triangle as a branching graph [PDF notes]
[Kerov, “Combinatorial examples in the theory of AF-algebras”],
[A. Borodin, G. Olsahnski “Representations of the Infinite Symmetric Group”],
these draft lecture notes
March 29, 2019
Arun Kannan - Diffusions from dynamics on the Pascal triangle
[arXiv:0706.1034, section 2]
April 5, 2019
No meeting
April 12, 2019
George Seelinger - A q-analogue of de Finetti’s theorem
[arXiv:0905.0367]
April 19, 2019
Liron Speyer - Young graph and its boundary
[A. Borodin, G. Olsahnski “Representations of the Infinite Symmetric Group”]
April 26, 2019
Joseph Eisner - Construction of extreme representations of the infinite symmetric group
Chapter 10, [A. Borodin, G. Olsahnski “Representations of the Infinite Symmetric Group”]