We introduce and study the notion of a Weyl module for the classical affine algebras, these
modules are universal finite-dimensional highest weight modules. We conjecture that the …

We introduce the shifted quantum affine algebras. They map homomorphically into the
quantized K-theoretic Coulomb branches of 3 d N= 4 3 d {\mathcal N= 4 SUSY quiver gauge …

This review is meant to be an account of the properties of the infinite-dimensional quantum
group (specifically, Yangian) symmetry lying behind the integrability of the AdS/CFT spectral …

We define an action of the braid group of a simple Lie algebra on the space of imaginary
roots in the corresponding quantum affine algebra. We then use this action to determine an …

0. Introduction. The canonical basis of the quantized universal envelo** algebra
associated to a simple finite-dimensional Lie algebra was introduced by Lusztig in [L2] via …

The fermionic formula conjectured by Kirillov and Reshetikhin describes the decomposition
(as a module for \boldsymbolU_\mathbfq\boldsymbol(\mathbfg\boldsymbol) of a tensor …

We prove the Kirillov–Reshetikhin (KR) conjecture in the general case: for all twisted
quantum affine algebras, we prove that the characters of KR modules solve the twisted Q …

Toroidal Braid Group Action and an Automorphism of Toroidal Algebra Uq(sln+1,tor) (n ≥
2) Page 1 Toroidal Braid Group Action and an Automorphism of Toroidal Algebra q sln 1Ytor …

The theory of Schur-Weyl duality has had a profound influence over many areas of algebra
and combinatorics. This text is original in two respects: it discusses affine q-Schur algebras …

We give a highest weight classification of the finite-dimensional irreducible representations
of twisted quantum affine algebras. As in the untwisted case, such representations are in …