Schur–Weyl duality for higher levels

By Jonathan Brundan, Alexander S. Kleshchev. 2006

117 citations recorded by the source corpus.

Abstract.We extend Schur–Weyl duality to an arbitrary level l ≥ 1, level one recovering the classical duality between the symmetric and general linear groups. In general, the symmetric group is replaced by the degenerate cyclotomic Hecke algebra over $${\mathbb{C}}$$ parametrized by a dominant weight of level l for the root system of type A∞. As an application, we prove that the degenerate analogue of the quasi-hereditary cover of the cyclotomic Hecke algebra constructed by Dipper, James and Mathas is Morita equivalent to certain blocks of parabolic category $${\mathcal{O}}$$ for the general linear Lie algebra.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c651a2b2044ed5365cecf3cf422ec74f530df8be

How researchers see this paper

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

In Discrete Mathematics and Combinatorics

1. Jonathan Brundan
2. I. Gordon
3. C. Stroppel
4. Raphaël Rouquier
5. I. Losev
6. E. Vasserot
7. P. Shan
8. M. Varagnolo

In Geometry and Topology

1. Ben Webster
2. I. Gordon
3. I. Losev
4. C. Stroppel
5. Jonathan Brundan
6. Raphaël Rouquier
7. Alexander S. Kleshchev
8. E. Vasserot

In Mathematical Physics

1. Ben Webster
2. Jonathan Brundan
3. C. Stroppel
4. Raphaël Rouquier
5. I. Losev
6. I. Gordon
7. E. Vasserot
8. Alexander S. Kleshchev

Citations in the corpus

• Nazarov–Wenzl algebras, coideal subalgebras and categorified skew Howe duality (2013, unknown): “This property plays an important role in the context of categorification of modules over quantum groups, [70], [17], [20].”
• Highest weight categories arising from Khovanov's diagram algebra II: Koszulity (2008, background): “or a regular block of O(m,n). Our new approach to the proof of this statement bypasses geometry KHOVANOV’S DIAGRAM ALGEBRA I 3 entirely: it is based instead on the generalised Schur-Weyl duality from [BK] which connects O(m,n) to degenerate cyclotomic Hecke algebras of level two. We actually prove a”
• Representation theory of symmetric groups and related Hecke algebras (2009, unknown): “We review the main features of that theory here referring the reader to [37, 39] for details.”
• On category O for cyclotomic rational Cherednik algebras (2011, background): “We thank R. Bezrukavnikov, J. Brundan, P. Etingof, A. Kleshchev, A. Kuznetsov and C. Stroppel for helpful discussions, the Research in Pairs programme at Oberwolfach where our work together began, and the Hausdorff Institute for Mathematics for the special semester on Representation Theory.”
• Categorifications and cyclotomic rational double affine Hecke algebras (2013, methodology): “The latter is closely related to the higher level Schur-Weyl duality studied by Brundan and Kleshchev in [7].”