An odd two-dimensional and a three-dimensional realization of Schur functions
Kohei Motegi (Tokyo University of Marine Science and Technology)
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.
mathematical physicsdynamical systemsquantum algebrarepresentation theorysymplectic geometry
Audience: general audience
BIMSA Integrable Systems Seminar
Series comments: The aim is to bring together experts in integrable systems and related areas of theoretical and mathematical physics and mathematics. There will be research presentations and overview talks.
Audience: Graduate students and researchers interested in integrable systems and related mathematical structures, such as symplectic and Poisson geometry and representation theory.
The zoom link will be distributed by mail, so please join the mailing list if you are interested in attending the seminar.
| Organizers: | NiŃolai Reshetikhin, Andrii Liashyk, Ivan Sechin, Andrey Tsiganov* |
| *contact for this listing |