### 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 language | English |
---|---|

Title of host publication | FPSAC Proceedings 2005 - 17th Annual International Conference on Formal Power Series and Algebraic Combinatorics |

Pages | 337-348 |

Number of pages | 12 |

Publication status | Published - 2005 |

Externally published | Yes |

Event | 17th Annual International Conference on Algebraic Combinatorics and Formal Power Series, FPSAC'05 - Taormina, Italy Duration: Jun 20 2005 → Jun 25 2005 |

### Other

Other | 17th Annual International Conference on Algebraic Combinatorics and Formal Power Series, FPSAC'05 |
---|---|

Country | Italy |

City | Taormina |

Period | 6/20/05 → 6/25/05 |

### Fingerprint

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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.

}

TY - GEN

T1 - Tableaux on periodic skew diagrams and irreducible representations of double affine Hecke algebra of type A

AU - Suzuki, Takeshi

AU - Vazirani, Monica

PY - 2005

Y1 - 2005

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84861125768&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84861125768&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84861125768

SP - 337

EP - 348

BT - FPSAC Proceedings 2005 - 17th Annual International Conference on Formal Power Series and Algebraic Combinatorics

ER -