Related papers: Crystal bases and simple modules for Hecke algebra…
We provide criteria for the cyclotomic quiver Hecke algebras of type C to be semisimple. In the semisimple case, we construct the irreducible modules.
We clarify the links between the graded Specht construction of modules over cyclotomic Hecke algebras and the RSK construction for quiver Hecke algebras of type A, that was recently imported from the setting of representations of p-adic…
We show that the category O for a rational Cherednik algebra of type A is equivalent to modules over a q-Schur algebra (parameter not a half integer), providing thus character formulas for simple modules. We give some generalization to…
Every double coset in $\text{GL}_m(k[[z]])\backslash \text{GL}_m(k((z)))/\text{GL}_m(k((z^2)))$ is uniquely represented by a block diagonal matrix with diagonal blocks in $\{1,z, \begin{pmatrix} 1& z\\ 0 &z^i \end{pmatrix} (i>1)\}$ if…
In this paper we compute the explicit value of the standard symmetrizing form of the cyclotomic Hecke algebra of type $G(\ell,1,n)$ on each Murphy basis element. We do this for both the non-degenerate cyclotomic Hecke algebra of type…
We study the action of the formal affine Hecke algebra on the formal group algebra, and show that the the formal affine Hecke algebra has a basis indexed by the Weyl group as a module over the formal group algebra. We also define a concept…
In this paper, we describe actions of standard generators on certain bases of simple modules for semisimple cyclotomic Hecke-Clifford superalgebras. As applications, we explicitly construct a complete set of primitive idempotents and…
For an almost split Kac-Moody group G over a local non-archimedean field, the last two authors constructed a spherical Hecke algebra H (over the complex numbers C, say) and its Satake isomorphism with the commutative algebra of Weyl…
We give an explicit expression for the central elements of affine Hecke algebras of type A in the Coxeter presentation, in terms of (parabolic) affine Kazhdan-Lusztig polynomials. Our approach is based on a version of quantum affine…
In this paper we prove theorems that describe how the representation theory of the affine Hecke algebra of type A and of related algebras such as the group algebra of the symmetric group are controlled by integrable highest weight…
Let $H_k(W,q)$ be the Iwahori--Hecke algebra associated with a finite Weyl group $W$, where $k$ is a field and $0 \neq q \in k$. Assume that the characteristic of $k$ is not ``bad'' for $W$ and let $e$ be the smallest $i \geq 2$ such that…
In this paper we define a two-variable, generic Hecke algebra, H, for each complex reflection group G(b,1,n). The algebra H specializes to the group algebra of G(b,1,n) and also to an endomorphism algebra of a representation of GL(n,q)…
For the quiver Hecke algebra $R$ associated with a simple Lie algebra, let $R$-gmod be the category of finite-dimensional graded $R$-modules. It is well-known that it categorifies the unipotent quantum coordinate ring. The localization of…
We give a $K$-theoretic realization of all affine Hecke algebras with two unequal parameters including exceptional types. This extends the celebrated work of Kazhdan and Lusztig, who gave a $K$-theoretic realization of affine Hecke algebras…
We establish geodesic normal forms for the general series of complex reflection groups G(de,e,n) by using the presentations of Corran-Picantin and Corran-Lee-Lee of G(e,e,n) and G(de,e,n) for d > 1, respectively. This requires the…
We determine the representation type of cyclotomic quiver Hecke algebras of affine type C. In the tame cases, we explicitly describe their basic algebras under the assumption $\text{ch}\ \mathbb{k}\ne2$, relying on the Morita invariance of…
We introduce a fermionic formula associated with any quantum affine algebra U_q(X^{(r)}_N). Guided by the interplay between corner transfer matrix and Bethe ansatz in solvable lattice models, we study several aspects related to…
The Lascoux-Leclerc-Thibon conjecture, reformulated and solved by S. Ariki, asserts that the K-group of the representations of the affine Hecke algebras of type A is isomorphic to the algebra of functions on the maximal unipotent subgroup…
We give a Morita equivalence theorem for so-called cyclotomic quotients of affine Hecke algebras of type B and D, in the spirit of a classical result of Dipper-Mathas in type A for Ariki-Koike algebras. As a consequence, the representation…
We define an extension of the affine Brauer algebra, the type B/C affine Brauer algebra. This new algebra contains the hyperoctahedral group and it naturally acts on $END_K(X \otimes V^{\otimes k})$ for Orthogonal and Symplectic groups.…