Resources: like the books in the library, you have the choice whether to open
them and read them, or let them sit on the shelf.
Professors and teachers fit in this category too.
Some of the material available from the links below is based upon work
supported by the Australian Research Council ARC grants DP0986774 and DP087995 and the US National Science Foundation under Grant No. 0353038 and
earlier awards. Any opinions, findings,
and conclusions or recommendations expressed in this material are those
of the author and do not necessarily reflect the views of these agencies.
E. Brieskorn and K. Saito,
Artin Groups and Coxeter Groups,
(with C. Coleman, R. Corran, J. Crisp, D. Easdown, R. Howlett and D. Jackson):
An English translation, with notes, of the paper
Artin-gruppen und Coxeter-gruppen
Inv. Math. 17 (1972) 245-271,
by E. Brieskorn and K. Saito.
I.V. Cherednik,
An analogue of the character formula for Hecke algebras,
Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 21, No. 2, pp. 94-95, April-June, 1987.
I.V. Cherednik,
Lectures on affine Khnizhnik-Zamolodchikov equations, quantum many body problems, Hecke algebras and Macdonald theory,
in collaborations wiht E. Date, K. Iohara, M. Jimbo, M. Kashiwara, T. Miwa, M. Noumi and Y. Saito, from lectures at IIAS Kyoto Japan 1997.
I.V. Cherednik,
Computation of monodromy of certain W-invariant local systems of types B, C, and D,
Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 24, No. 1, pp. 88-89, January-March, 1990.
Ivan Cherednik,
Notes on Affine Hecke Algebras I. (Degenerated Hecke Algebras and Yangians in Mathematical Physics), Lecture notes from lectures at Bonn University May-June 1990.
The thesis of P.N. Hoefsmit: Representations of Hecke Algebras of Finite Groups with BN-Pairs of Classical Type, University of British Columbia, 1974.
Steven A. Johnson, The Schubert Calculus and Eigenvalue Inequalities for Sums of Hermitian Matrices, Ph.D. Thesis, University of California, Santa Barbara, 1979, written under the supervision of Robert C. Thompson.
V.F.R Jones, The Potts model and the symmetric group
Subfactors: Proceedings of the Taniguchi Symposium on Operator Algebras
(Kyuzeso, 1993), River Edge, NJ, World Sci. Publishing, 1994, pp. 259–267.
David W. Koster's thesis: Complex Reflection groups, University of Wisconsin, Madison 1975, supervised by Louis Solomon
Kumar, Shrawan, Fusion product of positive level representations
and Lie algebra homology, from "Geometry and Physics" (ed. by J.E. Andersen et. al.), Lecture Notes in Pure and Applied Mathematics, vol. 184, Marcel Dekker, inc. New York-Basel-Hong Kong (1997), 253-259.
van der Lek's PhD Thesis: University of Nijmegen, September 1983, Supervised by E.J.N. Looijenga
I.G. Macdonald's book: Algebraic Geometry: Introduction to schemes, originally published by W.A. Benjamin, Inc 1968
- Contents,
Foreword,
Chapter 1: Introduction,
- Chapter 2: Irreducible and Noetherian topological spaces,
- Chapter 3: The spectrum of a commutative ring,
- Chapter 4: Presheaves and Sheaves,
- Chapter 5: Affine Schemes,
- Chapter 6: Preschemes,
- Chapter 7: Operations on Sheaves, quasicoherent and coherent sheaves,
- Chapter 8: Sheaf cohomology,
- Chapter 9: Cohomology of Affine Schemes,
- Chapter 10: The Riemann-Roch Theorem,
- Bibliography.
I.G. Macdonald's Notes on Kac-Moody Lie Algebras, a typed version of
handwritten lecture notes from 1983
I.G. Macdonald's Notes on Reflection Groups, a typed version of
handwritten lecture notes from a course at University of California,
San Diego, January-March 1991
I.G. Macdonald's Notes on Schubert polynomials,
originally published by LACIM, UQAM ????
- Contents,
- Foreword,
- Notes and References,
- Chapter 1: Permutations,
- Chapter 2: Divided differences,
- Chapter 3: MultiSchur functions,
- Chapter 4: Schubert polynomials 1,
- Chapter 5: Orthogonality,
- Chapter 6: Double Schubert polynomials,
- Chapter 7: Schubert polynomials 2,
- Appendix, Schubert varieties,
- Appendix: Combinatorial construction of Schubert polynomials,
I.G. Macdonald, Spherical functions on a Group of p-adic type, originally published by the University of Madras in November 1971.
Dale Peterson's MIT lecture notes on Quantum Cohomology of G/P, from Spring 1997
V.L. Popov, Discrete complex reflection groups, Lectures delivered at the Mathematical Institute, Rijksuniversteit Utrecht, October 1980.
L.D. Fadeev, N.Yu. Reshetikhin and L.A. Takhtajan, Quantization of Lie groups and Lie algebras, LOMI preprint 1987.
N.Yu. Reshetikhin, Quantized universal enveloping algebras, the Yang-Baxter equation and invariants of links I, LOMI preprint 1987.
J.P. Serre, Groupe finis d'automorphismes d'anneaux locaux réguliers, Ecole Normale Supérieure de Jeunes Filles, Colloque d'Algèbre [1967. Paris], no. 8 11 p. (translated to English by Arun Ram)
Steinberg's Yale Lecture Notes: Lectures on Chevalley groups, by Robert Steinberg, Yale University, 1967. Notes prepared by John Faulkner and Robert Wilson.
- Chapter 1: A basis for L,
- Chapter 2: A basis for U,
- Chapter 3: The Chevalley groups,
- Chapter 4: Simplicity of G,
- Chapter 5: Chevalley groups and algebraic groups,
- Chapter 6: Generators and relations,
- Chapter 7: Central extensions,
- Chapter 8: Variants of the Bruhat lemma,
- Chapter 9: The orders of the finite Chevalley groups,
- Chapter 10: Isomorphisms and Automorphisms,
- Chapter 11: Some twisted groups,
- Chapter 12: Representations,
- Chapter 13: Representations continued,
- Chapter 14: Representations concluded,
Thiem, Nat, Unipotent Hecke algebras: the structure, representation theory, and combinatorics, PhD Thesis, University of Wisconsin--Madison, 2004.
J. Tits, Les groupes simple de Suzuki et Ree, Séminaire N. Bourbaki, 1960-1961, exp. no. 210, p. 65-82, http://www.numdam.org/item?id=SB_1960-1961__6__65_0 (translated to English by Arun Ram)
Verma, Daya-Nand (1975), Role of Affine Weyl groups in the representation theory of Chevalley groups and their Lie algebras in Lie Groups and their Representations, ed. I.M.Gelfand, Halsted, New York, pp. 653-705.
E. Wiesner, Translation functors and the Shapovalov determinant,
PhD thesis, University of Wisconsin - Madison, 2005
A.V. Zelevinskii,
Two remarks on graded nilpotent classes,
Uspekhi Mat. Nauk 40 (1985), no. 1(241), 199–200.
English translation: Russian Math. Surveys 40 (1985), no. 1, 249–250.
A.V. Zelevinskii,
Resolvents, dual pairs, and character formulas,
Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 21, No. 2, pp. 74-75, April-June, 1987.
A.V. Zelevinskii,
p-adic analog of the Kazhdan-Lusztig Hypothesis, Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 15, No. 2, pp. 9-21, April-June, 1981.