相关论文: A projection property for Kazhdan-Lusztig bases
We show that the homology of a Temperley-Lieb algebra on an even number of strands has a rich algebraic structure and is highly nontrivial in general. This is achieved by proving that it is entirely governed by a differential graded…
We define and analyze various generalizations of the punctual Hilbert scheme of the plane, associated to complex or real Lie algebras. Out of these, we construct new geometric structures on surfaces whose moduli spaces share multiple…
In this paper we prove the Kazhdan-Lusztig type character formula for irreducible highest weight modules with positive rational highest weights over symmetrizable Kac-Moody Lie algebras.
Let $A$ be a unital commutative associative algebra over a field of characteristic zero, $\k$ be a Lie algebra, and $\z$ a vector space, considered as a trivial module of the Lie algebra $\g := A \otimes \k$. In this paper we give a…
In the recent papers with Masaki Kashiwara, the author introduced the notion of symmetric crystals and presented the Lascoux-Leclerc-Thibon-Ariki type conjectures for the affine Hecke algebras of type $B$. Namely, we conjectured that…
Kazhdan-Lusztig-Stanley polynomials are a combinatorial generalization of Kazhdan-Lusztig polynomials of for Coxeter groups that include g-polynomials of polytopes and Kazhdan-Lusztig polynomials of matroids. In the cases of Weyl groups,…
This paper continues the work which attempts to understand the general properties of the graded algebras associated with Hecke symmetries without a restriction on the parameter q of the Hecke relation imposed in earlier results.
We construct a monomial basis of a quantum affine algebra of simply-laced type, associated to the PBW basis of Beck-Nakajima. We show that there exists a simple algorithm of computing canonical basis in terms of the monomial basis. We…
Extensions of Lie algebras equipped with Sasakian or Frobenius-K\"ahler geometrical structures are studied. Conditions are given so that a double extension of a Sasakian Lie algebra be Sasakian again. Conditions are also given for obtaining…
The canonical basis for quantized universal enveloping algebras associated to the finite--dimensional simple Lie algebras, was introduced by Lusztig. The principal technique is the explicit construction (via the braid group action) of a…
Aiming for a revival of the theory of crystallographic complex reflection groups, we compute (minimal) Coxeter-like reflection presentations for the infinite families of those non-genuine groups which satisfy Steinberg's fixed point…
Construction of the diagrammatic version of the affine Temperley-Lieb algebra of type $\widetilde{A_N}$ as a subring of matrices over the Laurent polynomials is given. We move towards geometrical understanding of cellular structure of the…
We begin the study of the representation theory of the infinite Temperley-Lieb algebra. We fully classify its finite dimensional representations, then introduce infinite link state representations and classify when they are irreducible or…
We use the Perron-Frobenius Theorem to define, study and, in some sense, classify special simple modules over arbitrary finite dimensional positively based algebras. For group algebras of finite Weyl groups with respect to the…
It is well known that the Poisson Lie algebra is isomorphic to the Hamiltonian Lie algebra. We show that the Poisson Lie algebra can be embedded properly in the special type Lie algebra. We also generalize the Hamiltonian Lie algebra using…
Khovanov-Lauda-Rouquier algebras $R_\theta$ of finite Lie type are affine quasihereditary with standard modules $\Delta(\pi)$ labeled by Kostant partitions $\pi$ of $\theta$. In type $A$, we construct explicit projective resolutions of…
We give a combinatorial description of a new diagram algebra, the partial Temperley--Lieb algebra, arising as the generic centralizer algebra $\mathrm{End}_{\mathbf{U}_q(\mathfrak{gl}_2)}(V^{\otimes k})$, where $V = V(0) \oplus V(1)$ is the…
This paper is a report on a computer check of some positivity properties of the Hecke algebra in type H4, including the non-negativity of the coefficients of the structure constants in the Kazhdan-Lusztig basis. This answers a long-standing…
In a previous paper we introduced the notion of a D-Lie algebra $\tilde{L}$. A D-Lie algebra $\tilde{L}$ is an $A/k$-Lie-Rinehart algebra with a right $A$-module structure and a canonical central element $D$ satisfying several conditions.…
We generalize the definition of Yang-Baxter basis of type $A$ Hecke algebra introduced by A.Lascoux, B.Leclerc and J.Y.Thibon (Letters in Math. Phys., 40 (1997), 75--90) to all the Lie types and prove their duality. As an application we…