数学科学研究所
Insitute of Mathematical Science

Seminar: Virtual Coulomb branch and quantum K-theory

Seminar| Institute of Mathematical Sciences

Time: Monday, May 22nd, 2023 , 13:00-14:00
Location:IMS, RS408
Speaker: Zijun Zhou, Kavli IPMU

Abstract In this talk, I will discuss a virtual variant of the quantized Coulomb branch constructed by Braverman-Finkelberg-Nakajima, where the convolution product is modified by a virtual intersection. The resulting virtual Coulomb branch acts on the moduli space of quasimaps into the holomorphic symplectic quotient T^*N///G. When G is abelian, over the torus fixed points, this representation is a Verma module. The vertex function, a K-theoretic enumerative invariant introduced by A. Okounkov, can be expressed as a Whittaker function of the algebra. The construction also provides a description of the quantum q-difference module. As an application, this gives a proof of the invariance of the quantum q-difference module under the variation of GIT.



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