Journal ArticleDOI
Standard modules of quantum affine algebras
Michela Varagnolo,Eric Vasserot +1 more
Reads0
Chats0
TLDR
The authors gave a proof of the cyclicity conjecture of Akasaka and Kashiwara for simply-laced types via quiver varieties, and also gave an algebraic characterization of the standard modules.Abstract:
We give a proof of the cyclicity conjecture of Akasaka and Kashiwara for simply laced types, via quiver varieties. We also get an algebraic characterization of the standard modules.read more
Citations
More filters
Book
Quantum Groups and Quantum Cohomology
Davesh Maulik,Andrei Okounkov +1 more
TL;DR: In this article, a Hopf algebra Y_Q, the Yangian of Q, acting on the cohomology of Nakajima quiver varieties was constructed, and a formula for quantum multiplication by divisors in terms of this Yangian action was proved.
Journal ArticleDOI
On level-zero representation of quantized affine algebras
TL;DR: In this article, the authors studied the properties of level-zero modules over quantized affine algebras and proved that the universal extremal weight module with level zero fundamental weight as an extremal value is irreducible.
Journal ArticleDOI
Cherednik algebras, W-algebras and the equivariant cohomology of the moduli space of instantons on A 2
Olivier Schiffmann,Eric Vasserot +1 more
TL;DR: In this paper, a representation of the affine W-algebra of the group SU(r) on the equivariant homology space of the moduli space of U r -instantons is presented.
Journal ArticleDOI
Cluster algebras and quantum affine algebras
David Hernandez,Bernard Leclerc +1 more
TL;DR: In this article, the Grothendieck rings of a quantum affine algebra U q ( g ∧ ) of simply laced type were studied using cluster algebras.
Journal ArticleDOI
Weyl modules, Demazure modules, KR-modules, crystals, fusion products and limit constructions
TL;DR: In this article, it was shown that Kirillov?Reshetikhin modules and Weyl modules are in fact all Demazure modules and that the crystals of the Weyl module are the same up to some additional label zero arrows.
References
More filters
Book
Representation theory and complex geometry
Neil Chriss,Victor Ginzburg +1 more
TL;DR: This book discusses K-Theory, Symplectic Geometry, Flag Varieties, K- theory, and Harmonic Polynomials, and Representations of Convolution Algebras.
Journal ArticleDOI
Instantons on ALE spaces, quiver varieties, and Kac-Moody algebras
TL;DR: In this article, Kobayashi et al. introduced a new family of quiver varieties, which they call quiver variety, and studied their geometric structures, such as a natural *-action, symplectic geometry, topology, and so on.
Journal ArticleDOI
Introduction to Quantum Groups
P. Podleś,E. Müller +1 more
TL;DR: In this paper, the authors give an elementary introduction to the theory of algebraic and topological quantum groups (in the spirit of S. L. Woronowicz) and recall the basic facts from Hopf (*-) algebra theory, theory of compact (matrix) quantum groups and their actions on compact quantum spaces, and provide the most important examples, including the classification of quantum SL(2)-groups, their real forms and quantum spheres.
Journal ArticleDOI
Quiver varieties and finite dimensional representations of quantum affine algebras
TL;DR: In this article, a homomorphism Uq(Lg)→ KGw×C ∗ (Z(w))⊗Z[q,q−1] Q(q) 192 10. Relations (I) 194 11. Integral structure 214 13. Simple modules 224 15.