15 research outputs found
Multiplicative slices, relativistic Toda and shifted quantum affine algebras
We introduce the shifted quantum affine algebras. They map homomorphically
into the quantized -theoretic Coulomb branches of SUSY
quiver gauge theories. In type , they are endowed with a coproduct, and they
act on the equivariant -theory of parabolic Laumon spaces. In type ,
they are closely related to the open relativistic quantum Toda lattice of type
.Comment: 125 pages. v2: references updated; in section 11 the third local Lax
matrix is introduced. v3: references updated. v4=v5: 131 pages, minor
corrections, table of contents added, Conjecture 10.25 is now replaced by
Theorem 10.25 (whose proof is based on the shuffle approach and is presented
in a new Appendix). v6: Final version as published, references updated,
footnote 4 adde
Noncommutative Geometry in the Framework of Differential Graded Categories
In this survey article we discuss a framework of noncommutative geometry with
differential graded categories as models for spaces. We outline a construction
of the category of noncommutative spaces and also include a discussion on
noncommutative motives. We propose a motivic measure with values in a motivic
ring. This enables us to introduce certain zeta functions of noncommutative
spaces.Comment: 19 pages. Minor corrections and one reference added; to appear in the
proceedings volume of AGAQ Istanbul, 200
The degenerate analogue of Ariki's categorification theorem
We explain how to deduce the degenerate analogue of Ariki's categorification
theorem over the ground field C as an application of Schur-Weyl duality for
higher levels and the Kazhdan-Lusztig conjecture in finite type A. We also
discuss some supplementary topics, including Young modules, tensoring with
sign, tilting modules and Ringel duality.Comment: 44 page
The non-equivariant coherent-constructible correspondence and a conjecture of King
The coherent-constructible (CC) correspondence is a relationship between coherent sheaves on a toric variety X and constructible sheaves on a real torus T. This was discovered by Bondal and established in the equivariant setting by Fang, Liu, Treumann, and Zaslow. In this paper, we explore various aspects of the non-equivariant CC correspondence. Also, we use the non-equivariant CC correspondence to prove the existence of tilting complexes in the derived categories of toric orbifolds satisfying certain combinatorial conditions. This has applications to a conjecture of King
A quantum isomonodromy equation and its application to N=2 SU(N) gauge theories
We give an explicit differential equation which is expected to determine the
instanton partition function in the presence of the full surface operator in
N=2 SU(N) gauge theory. The differential equation arises as a quantization of a
certain Hamiltonian system of isomonodromy type discovered by Fuji, Suzuki and
Tsuda.Comment: 15 pages, v2: typos corrected and references added, v3: discussion,
appendix and references adde