Related papers: On reciprocal characters and the quantum affine Sc…

We study evaluation modules for quantum symmetric pair coideal subalgebras of affine type $\mathsf{AI}$. By computing the action of the generators in Lu and Wang's Drinfeld-type presentation on Gelfand-Tsetlin bases, we determine the…

We develop a $\mathtt{q}$-analogue of the theory of conjugation equivariant $\mathcal D$-modules on a complex reductive group $G$. In particular, we define quantum Hotta-Kashiwara modules and compute their endomorphism algebras. We use the…

We describe a correspondence (or duality) between the q-characters of finite-dimensional representations of a quantum affine algebra and its Langlands dual in the spirit of q-alg/9708006 and 0809.4453. We prove this duality for the…

We prove a super Frobenius formula for the characters of the cyclotomic Hecke algebras by applying the super Schur-Weyl reciprocity between the quantum superalgebras and cyclotomic Hecke algebras, which is a super analogue of the Frobenius…

For a Dynkin quiver $Q$ of type ADE and a sum $\beta$ of simple roots, we construct a bimodule over the quantum loop algebra and the quiver Hecke algebra of the corresponding type via equivariant K-theory, imitating…

We determine the set of dominant $\ell$--weights in the Weyl (or standard) modules for quantum affine $A_n$. We then prove that the space of homomorphisms between standard modules is at most one-dimensional and give a necessary and…

In this paper, we prove the Regev formulae for the characters of the Ariki--Koike algebras by applying the Schur--Sergeev reciprocity between the quantum superalgebras and the Ariki--Koike algebras, which is a generalization of the formulas…

Let $W$ be an affine Weyl group, and let $\Bbbk$ be a field of characteristic $p>0$. The diagrammatic Hecke category $\mathcal{D}$ for $W$ over $\Bbbk$ is a categorification of the Hecke algebra for $W$ with rich connections to modular…

Let $U_q'(\mathfrak{g})$ be a quantum affine algebra of arbitrary type and let $\mathcal{C}_{\mathfrak{g}}$ be Hernandez-Leclerc's category. We can associate the quantum affine Schur-Weyl duality functor $F_D$ to a duality datum $D$ in…

Many connections and dualities in representation theory can be explained using quasi-hereditary covers in the sense of Rouquier. The concepts of relative dominant and codominant dimension with respect to a module, introduced recently by the…

The integral formulae pertaining to the unitary group $\mathsf{U}(d)$ have been comprehensively reviewed, yielding fresh results and innovative proofs. Central to the derivation of these formulae lies the employment of Schur-Weyl duality, a…

As a natural generalization quantum Schur algebras associated with the Hecke algebra of the symmetric group, we introduce the quantum Schur superalgebra of type Q associated with the Hecke-Clifford superalgebra, which, by definition, is the…

Given a module $M$ for the algebra $\mathcal{D}_{\mathtt{q}}(G)$ of quantum differential operators on $G$, and a positive integer $n$, we may equip the space $F_n^G(M)$ of invariant tensors in $V^{\otimes n}\otimes M$, with an action of the…

We further develop the abstract representation theory of affine Hecke algebras with arbitrary positive parameters. We establish analogues of several results that are known for reductive p-adic groups. These include: the relation between…

Let us consider a specialization of an untwisted quantum affine algebra of type $ADE$ at a nonzero complex number, which may or may not be a root of unity. The Grothendieck ring of its finite dimensional representations has two bases,…

Let $W$ be a finite Weyl group of classical type which may not be irreducible, $F$ an algebraically closed field, $q$ an invertible element of $F$. We denote by $\mathcal H_W(q)$ the associated Hecke algebra. If $q=1$ then it is $FW$ and we…

In this paper we propose a new approach to tilting modules for reductive algebraic groups in positive characteristic. We conjecture that translation functors give an action of the (diagrammatic) Hecke category of the affine Weyl group on…

We give a new interpretation of representation theory of the finite-dimensional half-integer weight modules over the queer Lie superalgebra $\mathfrak{q}(n)$. It is given in terms of Brundan's work of finite-dimensional integer weight…

The partition algebra $\mathsf{P}_k(n)$ and the symmetric group $\mathsf{S}_n$ are in Schur-Weyl duality on the $k$-fold tensor power $\mathsf{M}_n^{\otimes k}$ of the permutation module $\mathsf{M}_n$ of $\mathsf{S}_n$, so there is a…

In the paper we consider the problem of computation of characters of relatively integrable irreducible highest weight modules $L$ over finite-dimensional basic Lie superalgebras and over affine Lie superalgebras $\mathfrak{g}$. The problems…