5 citations · 5 across the 3 of their papers we have counts for
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Constructible characters and canonical bases
Bernard Leclerc, Hyohe Miyachi
We give closed formulas for all vectors of the canonical basis of a level 2 irreducible integrable representation of . These formulas coincide at v=1 with Lusztig's…
Dual canonical bases, quantum shuffles and q-characters
Bernard Leclerc
Rosso and Green have shown how to embed the positive part of a quantum enveloping algebra in a quantum shuffle algebra. In this paper we study some properties of…
Imaginary vectors in the dual canonical basis of
Bernard Leclerc
Let be the maximal nilpotent subalgebra of a simple complex Lie algebra . We introduce the notion of imaginary vector in the dual canonical basis of , and we give ex…
Some closed formulas for canonical bases of Fock spaces
Bernard Leclerc, Hyohe Miyachi
We give some closed formulas for certain vectors of the canonical bases of the Fock space representation of U_v(sl^_n). As a result, a combinatorial description of certain paraboli…
Induced representations of affine Hecke algebras and canonical bases of quantum groups
Bernard Leclerc, Maxim Nazarov, Jean-Yves Thibon
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 canonical b…
Induced representations of affine Hecke algebras and singularities of R-matrices
Bernard Leclerc, Jean-Yves Thibon
We give an explicit criterion for the irreducibility of some induction products of evaluation modules of affine Hecke algebras of type A. This allows to describe the form of the si…