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Symmetric Functions & Probability Theory Seminar

Generalized Markov traces through algebra and geometry

Kostiantyn Tolmachov (University of Hamburg)

Location:  Hill Center 705
Date & time: Friday, 05 June 2026 at 12:10PM - 1:10PM

An important invariant of oriented links — the HOMFLY-PT polynomial — can be computed using a functional on the Iwahori-Hecke algebra of type A called Markov trace. This functional, constructed by Jones and Ocneanu, satisfies a trace-like property, as well as a certain compatibility with respect to the embeddings corresponding to the symmetric group embeddings S_2 -> S_3 -> ...
Markov traces are known to admit natural generalizations to Iwahori-Hecke algebras of arbitrary Coxeter type, via techniques from geometric representation theory and the theory of Soergel bimodules. In this talk, I will explain how some classical expressions for Markov traces in type A through the elementary symmetric polynomials in Jucys-Murphy elements, can be generalized to families of types B and D.

Based on a recent joint work with G. Zhylinskyi and earlier work with R. Bezrukavnikov