Heisenberg algebras and rational double affine Hecke algebras

By P. Shan, E. Vasserot. 2010

72 citations recorded by the source corpus.

In this paper we categorify the Heisenberg action on the Fock space via the category O of cyclotomic rational double affine Hecke algebras. This permits us to relate the filtration by the support on the Grothendieck group of O to a representation theoretic grading defined using the Heisenberg action. This implies a recent conjecture of Etingof.

Subfields: Algebra and Number Theory, Geometry and Topology, Spectroscopy

View Paper: https://www.semanticscholar.org/paper/aeb03d7b29196b32fae6fcd8d6d87316c3fe4c25

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. I. Gordon
2. I. Losev
3. Sabin Cautis
4. Anthony M. Licata
5. V. Ginzburg
6. Ben Webster
7. E. Gorsky
8. T. Arakawa

In Geometry and Topology

1. I. Losev
2. Sabin Cautis
3. I. Gordon
4. Anthony M. Licata
5. David E. V. Rose
6. Hoel Queffelec
7. V. Ginzburg
8. Ben Webster

In Spectroscopy

1. I. Losev
2. I. Gordon
3. Sabin Cautis
4. Anthony M. Licata

Citations in the corpus

• Categorifications and cyclotomic rational double affine Hecke algebras (2013, unknown): “[17,43,46].”
• On category O for cyclotomic rational Cherednik algebras (2011, methodology): “The results of [51] provide a count of the finite-dimensional irreducible Hp representations (see also [52]), and some families of finite-dimensional irreducible representations have been classified in [28], [25] and [33].”
• Heisenberg categorification and Hilbert schemes (2010, background): “So it is likely that the construction in [26] is complementary to our work.”