DATE2022-03-03 16:10-17:00

PLACE數學系館 1F3174教室

SPEAKER賴俊儒 研究員(中央研究院數學所

TITLESchur-Weyl Duality, Old and New

ABSTRACT In the beginning stage of representation theory, Schur's 1901 thesis on polynomial/rational representations of the general linear groups has played an influential role. A double centralizer property with the symmetric groups (i.e., Weyl groups of type A), now known as the Schur-Weyl duality, has been utilized to simultaneously study the representation theories of the ``holy trinity'' -- the symmetric groups, the (infinite-dimensional) general linear Lie algebras, and the finite-dimensional algebras known as the Schur algebras. Interests in Schur's ideas still continue nowadays, in a modern setting. In this talk I will focus on the quantum version of the duality, and go over the connections with the quantum groups via coordinate construction, with the Hecke algebras, and with rational Cherednik algebras.