Tableaux on periodic skew diagrams and irreducible representations of double affine Hecke algebra of type A

Takeshi Suzuki, Monica Vazirani

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The irreducible representations of the symmetric group Sn are parameterized by combinatorial objects called Young diagrams, or shapes. A given irreducible representation has a basis indexed by Young tableaux of that shape. In fact, this basis consists of weight vectors (simultaneous eigenvectors) for a commutative subalgebra F[X] of the group algebra FS n. The double affine Hecke algebra (DAHA) is a deformation of the group algebra of the affine symmetric group and it also contains a commutative subalgebra F[X]. Not every irreducible representation of the DAHA has a basis of weight vectors (and in fact it is quite difficult to parameterize all of its irreducible representations), but if we restrict our attention to those that do, these irreducible representations are parameterized by "affine shapes" and have a basis (of X-weight vectors) indexed by the "affine tableaux" of that shape. In this talk, we will construct these irreducible representations.

Original languageEnglish
Title of host publicationFPSAC Proceedings 2005 - 17th Annual International Conference on Formal Power Series and Algebraic Combinatorics
Pages337-348
Number of pages12
Publication statusPublished - 2005
Externally publishedYes
Event17th Annual International Conference on Algebraic Combinatorics and Formal Power Series, FPSAC'05 - Taormina, Italy
Duration: Jun 20 2005Jun 25 2005

Other

Other17th Annual International Conference on Algebraic Combinatorics and Formal Power Series, FPSAC'05
CountryItaly
CityTaormina
Period6/20/056/25/05

Fingerprint

Affine Hecke Algebra
Tableaux
Irreducible Representation
Skew
Diagram
Group Algebra
Symmetric group
Subalgebra
Young Tableaux
Young Diagram
Affine Group
Parameterise
Eigenvector

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Suzuki, T., & Vazirani, M. (2005). Tableaux on periodic skew diagrams and irreducible representations of double affine Hecke algebra of type A. In FPSAC Proceedings 2005 - 17th Annual International Conference on Formal Power Series and Algebraic Combinatorics (pp. 337-348)

Tableaux on periodic skew diagrams and irreducible representations of double affine Hecke algebra of type A. / Suzuki, Takeshi; Vazirani, Monica.

FPSAC Proceedings 2005 - 17th Annual International Conference on Formal Power Series and Algebraic Combinatorics. 2005. p. 337-348.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Suzuki, T & Vazirani, M 2005, Tableaux on periodic skew diagrams and irreducible representations of double affine Hecke algebra of type A. in FPSAC Proceedings 2005 - 17th Annual International Conference on Formal Power Series and Algebraic Combinatorics. pp. 337-348, 17th Annual International Conference on Algebraic Combinatorics and Formal Power Series, FPSAC'05, Taormina, Italy, 6/20/05.
Suzuki T, Vazirani M. Tableaux on periodic skew diagrams and irreducible representations of double affine Hecke algebra of type A. In FPSAC Proceedings 2005 - 17th Annual International Conference on Formal Power Series and Algebraic Combinatorics. 2005. p. 337-348
Suzuki, Takeshi ; Vazirani, Monica. / Tableaux on periodic skew diagrams and irreducible representations of double affine Hecke algebra of type A. FPSAC Proceedings 2005 - 17th Annual International Conference on Formal Power Series and Algebraic Combinatorics. 2005. pp. 337-348
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