TRINO

Speaker: Sachin Gautam (Ohio State University)

Title: Lattice operators of the quantum affine algebra

When: November 7 @ 14h00

Where: Dubrovin lecture room 136, SISSA, via Bonomea 265, Trieste

Abstract: Let g be a finite-dimensional, simple Lie algebra over the field of complex numbers, and U be the quantum, untwisted affine algebra, associated to g. Via Lusztig's q-exponential formulae, it is well known that the affine braid group of g acts on any integrable representation of U. In particular, one obtains an action of the coroot lattice of g on such a representation.  In this talk, I will present an explicit formula for these lattice operators on finite-dimensional representations of U, in terms of the generators of its maximal commutative subalgebra in Drinfeld's loop presentation. Time permitting, I will discuss some applications towards the universal R-matrix of the quantum affine algebra, monodromy of the trigonometric Casimir connection, and geometry of Nakajima quiver varieties. This formula was obtained in a recent joint work with V. Toledano Laredo (arxiv:2501.2365).