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BIMSA Integrable Systems Seminar
An odd two-dimensional and a three-dimensional realization of Schur functions
An odd two-dimensional and a three-dimensional realization of Schur functions
Organizers
Speaker
Kohei Motegi
Time
Tuesday, November 19, 2024 4:00 PM - 5:00 PM
Venue
A6-101
Online
Zoom 873 9209 0711
(BIMSA)
Abstract
We present unconventional constructions of Schur/Grothendieck polynomials from the viewpoint of quantum integrability.
First, we present a construction of Schur/Grassmannian Grothendieck polynomials using a degeneration of higher rank rational/quantum R-matrices, which is different from the Bethe vector or Fomin-Kirillov type constructions.
Second, using the q=0 version of the three-dimensional $R$-matrix satisfying the tetrahedron equation introduced by
Bazhanov-Sergeev and further studied by Kuniba-Maruyama-Okado, we show that a class of three-dimensional partition functions
can be expressed as Schur polynomials. Keys of our derivation in both constructions are the multiple commutation relations between quantum algebras.
Partly based on joint work with Shinsuke Iwao and Ryo Ohkawa.
First, we present a construction of Schur/Grassmannian Grothendieck polynomials using a degeneration of higher rank rational/quantum R-matrices, which is different from the Bethe vector or Fomin-Kirillov type constructions.
Second, using the q=0 version of the three-dimensional $R$-matrix satisfying the tetrahedron equation introduced by
Bazhanov-Sergeev and further studied by Kuniba-Maruyama-Okado, we show that a class of three-dimensional partition functions
can be expressed as Schur polynomials. Keys of our derivation in both constructions are the multiple commutation relations between quantum algebras.
Partly based on joint work with Shinsuke Iwao and Ryo Ohkawa.