✦ LIBER ✦

Graded Multiplicities in the Exterior Algebra

✍ Scribed by Yuri Bazlov

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 217 KB
Volume: 158
Category: Article
ISSN: 0001-8708
DOI: 10.1006/aima.2000.1969

No coin nor oath required. For personal study only.

✦ Synopsis

This paper deals with the graded multiplicities of the ``smallest'' irreducible representations of a simple Lie algebra in its exterior algebra. An explicit formula for the graded multiplicity of the adjoint representation in terms of the Weyl group exponents was conjectured by A. Joseph; a proof of this conjecture, based on the properties of Macdonald polynomials, is given in the present paper. The same method allows us to calculate the multiplicity of the simple module with highest weight equal to the short dominant root.

📜 SIMILAR VOLUMES

The Residue Complex of a Noncommutative

The Residue Complex of a Noncommutative Graded Algebra

✍ Amnon Yekutieli 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 258 KB

The Entropy of Graded Algebras

✍ M.F Newman; Csaba Schneider; Aner Shalev 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 122 KB

Presenting the Graded Lie Algebra Associ

Presenting the Graded Lie Algebra Associated to the Nottingham Group

✍ A. Caranti 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 273 KB

The graded Lie algebra L associated to the Nottingham group is a loop algebra ôf the Witt algebra W . The universal covering W of W has one-dimensional 1 1 1 ĉentre, so that the corresponding loop algebra M of W has an infinite-dimen-1 Ž . Ž . sional centre Z M . As MrZ M is isomorphic to L, it foll

Integrable Roots in Split Graded Lie Alg

Integrable Roots in Split Graded Lie Algebras

✍ Karl-Hermann Neeb 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 314 KB

A Lie algebra is said to be split graded if it is graded by a torsion free abelian group Q in such a way that the subalgebra 0 is abelian and the operators ad 0 are diagonalized by the grading. The elements of Q \ 0 with α = 0 are called roots and a root α is said to be integrable if there are root

ℤ × ℤ-Graded Lie Algebras Generated by t

ℤ × ℤ-Graded Lie Algebras Generated by the Virasoro Algebra and sl2

✍ Yucai Su; Jiangfeng Zhang; Kaiming Zhao 📂 Article 📅 2002 🏛 John Wiley and Sons 🌐 English ⚖ 214 KB

On the Classification of Strongly Graded

On the Classification of Strongly Graded Hopf Algebras

✍ Antonio M. Cegarra 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 113 KB

The main result in this paper states that every strongly graded bialgebra whose component of grade 1 is a finite-dimensional Hopf algebra is itself a Hopf algebra. This fact is used to obtain a group cohomology classification of strongly graded Hopf algebras, with 1-component of finite dimension, fr