The Role of Affine Weyl groups in the representation theory of algebraic Chevalley groups and their Lie algebras

Arun Ram
Department of Mathematics and Statistics
University of Melbourne
Parkville, VIC 3010 Australia
aram@unimelb.edu.au

Last update: 1 April 2014

Contents

§ 0. Introduction Part I. A conjecture on Weyl's dimension polynomial § 1. Affine Weyl groups
§ 2. Harmonic polynomials and Conjecture I
§ 3. Evidence in low ranks Part II. Representations and decompositions in characteristic $p\ne 0$ § 4. Fundamental constants $c_{\lambda \mu }$ and the character formula
§ 5. The "Harish-Chandra principle" and two conjectures on $c_{\lambda \mu }$
§ 6. PIM's of the $u\text{-algebra}$ and Humphreys' numbers $d_{\lambda }$
§ 7. Conjecture on the decomposition of induced modules $Z_{\lambda }$
§ 8. Epilogue: A metamathematical (?) conjecture

Notes and References

This is an excerpt of the paper The Role of Affine Weyl groups in the representation theory of algebraic Chevalley groups and their Lie algebras by Daya-Nand Verma. It appeared in Lie Groups and their Representations, ed. I.M.Gelfand, Halsted, New York, pp. 653–705, (1975).

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