Smallness problem for quantum affine algebras and quiver varieties
نویسندگان
چکیده
منابع مشابه
Smallness Problem for Quantum Affine Algebras and Quiver Varieties
The geometric small property (Borho-MacPherson [BM]) of projective morphisms implies a description of their singularities in terms of intersection homology. In this paper we solve the smallness problem raised by Nakajima [N8, N6] for certain resolutions of quiver varieties [N8] (analogs of the Springer resolution) : for Kirillov-Reshetikhin modules of simply-laced quantum affine algebras, we ch...
متن کاملQuiver Varieties and Finite Dimensional Representations of Quantum Affine Algebras
Introduction 145 1. Quantum affine algebra 150 2. Quiver variety 155 3. Stratification of M0 163 4. Fixed point subvariety 167 5. Hecke correspondence and induction of quiver varieties 169 6. Equivariant K-theory 174 7. Freeness 178 8. Convolution 185 9. A homomorphism Uq(Lg)→ KGw×C ∗ (Z(w))⊗Z[q,q−1] Q(q) 192 10. Relations (I) 194 11. Relations (II) 202 12. Integral structure 214 13. Standard m...
متن کاملQUIVER VARIETIES AND t–ANALOGS OF q–CHARACTERS OF QUANTUM AFFINE ALGEBRAS
Let us consider a specialization of an untwisted quantum affine algebra of type ADE at a nonzero complex number, which may or may not be a root of unity. The Grothendieck ring of its finite dimensional representations has two bases, simple modules and standard modules. We identify entries of the transition matrix with special values of “computable” polynomials, similar to Kazhdan-Lusztig polyno...
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Motivated by a recent conjecture by Hernandez and Leclerc [30], we embed a Fomin-Zelevinsky cluster algebra [20] into the Grothendieck ring R of the category of representations of quantum loop algebras Uq(Lg) of a symmetric Kac-Moody Lie algebra, studied earlier by the author via perverse sheaves on graded quiver varieties [48]. Graded quiver varieties controlling the image can be identified wi...
متن کاملHandsaw Quiver Varieties and Finite W -algebras
Following Braverman–Finkelberg–Feigin–Rybnikov (arXiv: 1008.3655), we study the convolution algebra of a handsaw quiver variety, a.k.a. a parabolic Laumon space, and a finite W -algebra of type A. This is a finite analog of the AGT conjecture on 4-dimensional supersymmetric Yang–Mills theory with surface operators. Our new observation is that the C-fixed point set of a handsaw quiver variety is...
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ژورنال
عنوان ژورنال: Annales scientifiques de l'École normale supérieure
سال: 2008
ISSN: 0012-9593,1873-2151
DOI: 10.24033/asens.2068