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

Last update: 1 April 2014

## References

[BGG1971] I.N. Bernstein, I.M. Gel’fand and S.I. Gel’fand, The structure of representations generated by vectors of highest weight, 1971.
*This reference was mostly in russian and couldn't be copied.

[Bor1970] A. Borel, Properties and linear representations of Chevalley groups, in Seminar on algebraic groups and related finite groups, Springer Lecture Notes, Vol 131, 1970.

[Bou1968] N. Bourbaki, Groupes et Algébres de Lie, Chapitres 4, 5 et 6, Eléments de Mathématique, 34, Hermann, Paris, (1968). MR 39:1590

[Bra1967] B. Braden, Restricted representations of classical Lie algebras of type ${A}_{2}$ and ${B}_{2}$, Bull. Amer. Math. Soc., 73 (1967), 482-486.

[Cur1960] C.W. Curtis, On projective representations of certain finite groups, Proc. Amer. Math. Soc., 11 (1960), 852-860.

[Gel1971] I. M. Gelfand, The cohomology of infinite dimensional Lie algebras; some questions in integral geometry, in Actes, Congrès intern. math., 1970, Vol. 1, pp. 95-111, Gauthier-Villars, Paris, 1971.

[Hum1971] J.E. Humphreys, Modular representations of classical Lie algebras and semisimple groups, J. Algebra, 19 (1971), 51-79.

[HVe1973] J.E. Humphreys and D.-N. Verma, Projective modules for finite Chevalley groups, Bull. Amer. Math. Soc, 79 (1973), 467-468.

[IMa1965] N. Iwahori, H. Matsumoto, On some Bruhat decomposition and the structure of the Hecke rings of $p\text{-adic}$ Chevalley groups, Publ. Math. I.H.E.S. 25 (1965) 5-48 or 237-280.

[Spr1968] T.A. Springer, Weyl's character formula for algebraic groups, Inventiones Math., 5 (1968), 85-105.

[Ste1964] R. Steinberg, Differential equations invariant under finite reflection reflection groups, Trans. Amer. Math. Soc. 112 (1964), 392–400. MR 29:4807

[Ste1968-2] R. Steinberg, Endomorphisms of linear algebraic groups, Mem. Amer. Math. Soc. 80 (1968) 1–108.

[Ste1968] R. Steinberg, Lectures on Chevalley groups, Notes prepared by John Faulkner and Robert Wilson, Yale University, New Haven, CT, 1968.

[Vel1970] F. D. Veldkamp, Representations of algebraic groups of type ${F}_{4}$ in characteristic 2, J. Algebra, 16 (1970), 326-339.

[Ver1966] D.-N. Verma, Structure of certain induced representations of complex semisimple Lie algebras, Dissertation, Yale University, New Haven, 1966.

[Ver1968] D.-N. Verma, Structure of certain induced representations of complex semisimple Lie algebras, (announcement of [Ver1966]), Bull. Amer. Math. Soc., 74 (1968), 160-166.

[Ver1971] D.-N. Verma, Möbius inversion for the Bruhat ordering on a Weyl group, Ann. Sci. École Norm. Sup. ${4}^{\circ }$-série, 4 (1971), 393-398.

[Ver1972] D.-N. Verma, A strengthening of the exchange property of Coxeter groups, to appear, 1972.

[Ver1972-2] D.-N. Verma, A note on Chevalley lattice and its Kostant envelope, in preparation, 1972.

[Ver1972-3] D.-N. Verma, Exponentiating the projective modules of the $u\text{-algebra}$ associated to an algebraic Chevalley group, in preparation, 1972.

[Won1971] W. J. Wong, Representations of Chevalley groups in characteristic $p$, in Proc. of Symposia in Pure Mathematics, Vol. XXI, AMS, Providence, 1971.

## 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).