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Seminars and Lectures




Київський математичний колоквіум

Organiser: КМТ
Location: Інститут математики НАНУ, 305, 15.00
Date Seminar
22, February 2019
15:00 Friday
Узагальнена дуальність Шура-Вейля
Ювал Флікер (Arial University, Israel)

A duality theorem in mathematics relates two seemingly unrelated objects: this is its attraction. An early example was discovered by Schur in his 1901 Berlin thesis. He found a relation between representations of the symmetric group S_d, and those of GL(n). A super analogue, reminiscent of bosons and fermions, involving the supergroup GL(m|n), followed. In influential works of 1986, Drinfeld and Jimbo extended Schur’s duality to relate representations of the quantum general linear group, with those of the Hecke algebra, the latter defined using their universal R-matrices solutions of the Yang-Baxter equations. Chari and Pressley then studied the affine case. I shall attempt to describe the ultimate extension, to the super affine quantum situation. In particular I construct a functor relating suitable categories of affine Hecke modules - important in number theory - and of affine quantum supergroups - from physics, as a modern twist of Schur\'s duality, afforded by Yamane\'s presentation of these supergroups.
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