𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Hecke Algebras of TypeAwithq=−1

✍ Scribed by Gordon James; Andrew Mathas

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
537 KB
Volume
184
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper we study the decomposition matrices of the Hecke algebras of type A with q s y1 over a field of characteristic 0. We give explicit formulae for the columns of the decomposition matrices indexed by all 2-regular partitions with 1 or 2 parts and an algorithm for calculating the columns of the decomposition matrix indexed by partitions with 3 parts. Combining these results we find all of the rows of the decomposition matrices which are indexed by partitions with at most four parts. All this is accomplished by means of a more general theory which begins by showing that the decomposition numbers in the columns of the decomposition matrices indexed by 2-regular partitions with ''enormous 2-cores'' are Littlewood᎐ Richardson coefficients.

📜 SIMILAR VOLUMES

Hecke Algebras and Semisimplicity of Mon
Hecke Algebras and Semisimplicity of Monoid Algebras
✍ Mohan S Putcha 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 140 KB

We begin by constructing Hecke algebras for arbitrary finite regular monoids M. We then show that the semisimplicity of the complex monoid algebra ‫ރ‬ M is equivalent to the semisimplicity of the associated Hecke algebras and a condition on induced group characters. We apply these results to finite

Semisimplicity of Parabolic Hecke Algebr
Semisimplicity of Parabolic Hecke Algebras
✍ Yasushi Gomi 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 212 KB

The semisimplicity of Iwahori᎐Hecke algebras has been studied by several Ž . authors. A. Gyoja J. Algebra 174, 1995, 553᎐572 gave a necessary and sufficient condition for Iwahori᎐Hecke algebras to be semisimple, using the modular repre-Ž . sentation theory. The author J. Algebra 183, 1996, 514᎐544 s

Residue Construction of Hecke Algebras
Residue Construction of Hecke Algebras
✍ Victor Ginzburg; Mikhail Kapranov; Eric Vasserot 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 393 KB

Hecke algebras are usually defined algebraically, via generators and relations. We give a new algebra-geometric construction of affine and double-affine Hecke algebras (the former is known as the Iwahori Hecke algebra, and the latter was introduced by Cherednik) in terms of residues. More generally,

Symmetric Cyclotomic Hecke Algebras
Symmetric Cyclotomic Hecke Algebras
✍ Gunter Malle; Andrew Mathas 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 236 KB

In this paper we prove that the generic cyclotomic Hecke algebras for imprimitive complex reflection groups are symmetric over any ring containing inverses of the parameters. For this we show that the determinant of the Gram matrix of a certain canonical symmetrizing form introduced by K. Bremke and

Units in Hecke Algebras
Units in Hecke Algebras
✍ Dean Alvis 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 144 KB

This paper investigates the conditions under which elements of a standard spanning set of the Hecke algebra of an induced character of a finite group are units. General criteria are developed, as well as results that apply to induced linear characters, permutation representations of nilpotent groups