Related papers: A projection property for Kazhdan-Lusztig bases
We define canonical bases of the higher-level q-deformed Fock space modules of the affine Lie algebra sl(n)^. This generalizes the result of Leclerc and Thibon for the case of level 1. We express the transition matrices between the…
We study a two-boundary extension of the Temperley-Lieb algebra which has recently arisen in statistical mechanics. This algebra lies in a quotient of the affine Hecke algebra of type C and has a natural diagrammatic representation. The…
We determine the structure of two variations on the Temperley-Lieb algebra, both used for dealing with special kinds of boundary conditions in statistical mechanics models. The first is a new algebra, the `blob' algebra (the reason for the…
In [Tame_quivers_and_affine_bases_I], we give a Ringel-Hall algebra approach to the canonical bases in the symmetric affine cases. In this paper, we extend the results to general symmetrizable affine cases by using Ringel-Hall algebras of…
This is an extended and corrected version of the author's Diplomarbeit. A class of algebras called generic pro-$p$ Hecke algebras is introduced, enlarging the class of generic Hecke algebras by considering certain extensions of (extended)…
We show that there is a unique Markov trace on the tower of Temperley--Lieb type quotients of Hecke algebras of Coxeter type $E_n$ (for all $n \geq 6$). We explain in detail how this trace may be computed easily using tom Dieck's calculus…
We study classes determined by the Kazhdan-Lusztig basis of the Hecke algebra in the $K$-theory and hyperbolic cohomology theory of flag varieties. We first show that, in $K$-theory, the two different choices of Kazhdan-Lusztig bases…
In this article, we prove the $p$-adic Kazhdan-Lusztig hypothesis for $\mathrm{GL}_n(F)$. While the approach via graded affine Hecke algebras due to recent work of Solleveld leads to more general results, this article serves to completes…
In an earlier work, we defined a ``generalised Temperley-Lieb algebra'' $TL_{r,1,n}$ corresponding to the imprimitive reflection group $G(r,1,n)$ as a quotient of the cyclotomic Hecke algebra. In this work we introduce the generalised…
In the framework of canonical and dual canonical bases of Fock spaces, Brundan in 2003 formulated a Kazhdan-Lusztig type conjecture for the characters of the irreducible and tilting modules in the BGG category for the general linear Lie…
For the BGG category of $\mathfrak{q}(n)$-modules of half-integer weights, a Kazhdan-Lusztig conjecture \`a la Brundan is formulated in terms of categorical canonical basis of the $n$th tensor power of the natural representation of the…
We classify non-operatorial matrices K solving Skylanin's quantum reflection equation for all R-matrices obtained from the newly defined general rank- n Hadamard type representations of the Temperley-Lieb algebra $TL_N(\sqrt n)$. They are…
We deduce the Kazhdan-Lusztig conjecture on the multiplicities of simple modules over a simple complex Lie algebra in Verma modules in category O from the equivariant geometric Satake correspondence and the analysis of torus fixed points in…
We consider some bases in the Hecke algebra and exhibit certain dualities between them.
Using a characterization of a generalized $\tau$-invariant for intermediate parameter Hecke algebras in type $B_n$, we verify a conjectural description of Kazhdan-Lusztig cells in this setting due to C. Bonnaf\'e, L. Iancu, M. Geck, and T.…
In this paper, we mainly study the generalized Heisenberg-Virasoro algebra. Some structural properties of the Lie algebra are studied.
Let (W,S) be a Coxeter system of affine type D, and let TL(W) the corresponding generalized Temperley-Lieb algebra. In this extended abstract we define an infinite dimensional associative algebra made of decorated diagrams which is…
This is a companion article to my papers on Kazhdan-Lusztig polynomials and character formulae for the Lie superalgebras gl(m|n) (much revised!) and q(n). The goal is to develop the general theory of tilting modules for Lie superalgebras,…
Under a suitable hypothesis, we construct a full set of pairwise orthogonal maximal vectors in $V^{\otimes n}$, where $V=V(1)$ is the simple module of highest weight $1$ for the quantized enveloping algebra $\mathbf{U}(\mathfrak{sl}_2)$. We…
From the combinatorial characterizations of the right, left, and two-sided Kazhdan-Lusztig cells of the symmetric group, 'RSK bases' are constructed for certain quotients by two-sided ideals of the group ring and the Hecke algebra.…