970 research outputs found
A Littlewood-Richardson rule for evaluation representations of quantum affine sl(n)
We give a combinatorial description of the composition factors of the
induction product of two evaluation modules of the affine Iwahori-Hecke algebra
of type GL(m). Using quantum affine Schur-Weyl duality, this yields a
combinatorial description of the composition factors of the tensor product of
two evaluation modules of the quantum affine algebra of type sl(n)
Cluster algebras and representation theory
We apply the new theory of cluster algebras of Fomin and Zelevinsky to study
some combinatorial problems arising in Lie theory. This is joint work with
Geiss and Schr\"oer (3, 4, 5, 6), and with Hernandez (8, 9)
Constructible characters and canonical bases
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 formulas for the constructible characters of the
Iwahori-Hecke algebras of type B and D.Comment: 16 page
Monoidal categorifications of cluster algebras of type A and D
In this note, we introduce monoidal subcategories of the tensor category of
finite-dimensional representations of a simply-laced quantum affine algebra,
parametrized by arbitrary Dynkin quivers. For linearly oriented quivers of
types A and D, we show that these categories provide monoidal categorifications
of cluster algebras of the same type. The proof is purely
representation-theoretical, in the spirit of [arXiv:0903.1452].Comment: 15 pages ; to appear in the proceedings of the Conference Symmetries,
Integrable systems and Representation
Nakajima varieties and repetitive algebras
We realize certain graded Nakajima varieties of finite Dynkin type as orbit
closures of repetitive algebras of Dynkin quivers. As an application, we obtain
that the perverse sheaves introduced by Nakajima for describing irreducible
characters of quantum loop algebras are isomorphic to the intersection
cohomology sheaves of these orbit closures.Comment: 26 pages, v2 : Minor corrections. Final version to appear in PRIMS
(Publications of the Research Institute for Mathematical Sciences, Kyoto
Aggregation and residuation
In this paper, we give a characterization of meet-projections in simple atomistic lattices that generalizes results on the aggregation of partitions in cluster analysis.Aggregation theory ; dependence relation ; meet projection ; partition ; residual map ; simple lattice
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