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We show that the Littlewood-Richardson coefficients are values at 1 of certain parabolic Kazhdan-Lusztig polynomials for affine symmetric groups. These q-analogues of Littlewood-Richardson multiplicities coincide with those previously introduced in [21] in terms of ribbon tableaux.

We introduce a new family of symmetric functions, which are defined in terms of ribbon tableaux and generalize Hall-Littlewood functions. We present a series of conjectures, and prove them in two special cases.

- Bernard Leclerc
- 1998

Let C be the category of finite-dimensional representations of a quantum affine algebra U q (g) of simply-laced type. We introduce certain monoidal subcategories C ℓ (ℓ ∈ N) of C and we study their Grothendieck rings using cluster algebras.

- Daniel Krob, Bernard Leclerc, Jean-Yves Thibon
- IJAC
- 1997

Noncommutative analogues of classical operations on symmetric functions are investigated , and applied to the description of idempotents and nilpotents in descent algebras. Its is shown that any sequence of Lie idempotents (one in each descent algebra) gives rise to a complete set of indecomposable orthogonal idempotents of each descent algebra, and various… (More)

- Christof Geiss, Bernard Leclerc, Jan Schr¨oer
- 2008

Let n be a maximal nilpotent subalgebra of a complex simple Lie algebra of type A, D, E. Lusztig has introduced a basis of U (n) called the semicanonical basis, whose elements can be seen as certain constructible functions on varieties of modules over a preprojective algebra of the same Dynkin type as n. We prove a formula for the product of two elements of… (More)

- Christof Geiss, Bernard Leclerc, Jan Schr¨oer
- 2005

Let Λ be a preprojective algebra of simply laced Dynkin type ∆. We study maximal rigid Λ-modules, their endomorphism algebras and a mutation operation on these modules. This leads to a representation-theoretic construction of the cluster algebra structure on the ring C[N ] of polynomial functions on a maximal unipotent subgroup N of a complex Lie group of… (More)

A criterion of irreducibility for induction products of evaluation modules of type A affine Hecke algebras is given. It is derived from multiplicative properties of the cano-nical basis of a quantum deformation of the Bernstein-Zelevinsky ring.

- Alain Lascoux, Bernard Leclerc, Jean-Yves Thibon
- Eur. J. Comb.
- 1994

- Christof Geiss, Bernard Leclerc, Jan Schr¨oer
- 2008

Let Q be a finite quiver without oriented cycles, and let Λ be the associated preprojective algebra. To each terminal CQ-module M (these are certain preinjective CQ-modules), we attach a natural subcategory CM of mod(Λ). We show that CM is a Frobenius category, and that its stable category C M is a Calabi-Yau category of dimension two. Then we develop a… (More)