Geometric Construction of Representations of Affine Algebras

By H. Nakajima. 2002

47 citations recorded by the source corpus.

Let be a finite subgroup of SL 2(C). We consider -fixed point sets in Hilbert schemes of points on the affine planeC 2 . The direct sum of homology groups of components has a structure of a representation of the affine Lie algebra b corresponding to . If we replace homology groups by equivar iant K-homology groups, we get a representation of the quantum toroidal algebra Uq(Lb g). We also discuss a higher rank generalization and character formulas in terms of intersection homology groups.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/01c57f75879c051723d10a1bfccde43ed454e465

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. S. Shatashvili
2. Vasily Pestun
3. N. Nekrasov

In Geometry and Topology

1. N. Nekrasov
2. Vasily Pestun
3. S. Shatashvili
4. C. Vafa
5. Hee-Cheol Kim
6. Yuji Tachikawa
7. D. Gaiotto
8. A. Klemm

In Mathematical Physics

1. S. Shatashvili
2. Vasily Pestun
3. N. Nekrasov
4. C. Vafa
5. Marcos Mariño
6. Yuji Tachikawa
7. J. Teschner
8. A. Klemm

Citations in the corpus

• Quantum Geometry and Quiver Gauge Theories (2013, methodology): “[133] H. Nakajima, “t-analogs of q-characters of quantum affine algebras of type E6, E7, E8,”. http://dx.doi.org/10.1007/978-0-8176-4697-4_10.”
• Quiver varieties and cluster algebras (2009, unknown): “From the definition of σW in the formula (4.9) it is clear that σW is unchanged even if we add ±(1, 1) to (dim Wi, dim Wi′) for i ∈ I1.”