Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-22T06:44:30.103Z Has data issue: false hasContentIssue false
  • English
  • Français

A Survey of the Work of George Lusztig

Published online by Cambridge University Press:  11 January 2016

R. W. Carter
R. W. Carter*
Affiliation:
Mathematics Research Centre, University of Warwick, Coventry CV4 7AL, United Kingdom, [email protected]
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It is an honour to be invited to contribute a survey article on the work of George Lusztig in celebration of his 60th birthday.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 182: Special Issue Celebrating the 60th Birthday of George Lusztig , June 2006 , pp. 1 - 45
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2006

References

References

Section 3

Lusztig, G., The discrete series of GLn over a finite field, Ann. Math. Studies 81, Princeton Univ. Press, 1974, 99 pp.Google Scholar
Carter, R. W. and Lusztig, G., On the modular representations of the general linear and symmetric groups, Math. Zeit., 136 (1974), 193–242.Google Scholar

Section 4

Deligne, P. and Lusztig, G., Representations of reductive groups over finite fields, Ann. Math., 103 (1976), 103–161.Google Scholar

Section 5, 6, 7

Howlett, R. B. and Lehrer, G. I., Induced cuspidal representations and generalized Hecke rings, Invent. Math., 58 (1980), 37–64.Google Scholar
Lusztig, G., Characters of reductive groups over a finite field, Ann. Math. Studies 107, Princeton Univ. Press, 1984, 384 pp.Google Scholar
Carter, R. W., Finite Groups of Lie Type (Conjugacy classes and complex characters), Wiley Classics Library, 1985, 544 pp.Google Scholar
Digne, F. and Michel, J., Representations of Finite Groups of Lie Type, London Math. Soc. Student Texts 21, 1991, 159 pp.Google Scholar
Geck, M., Finite groups of Lie type, Representations of Reductive Groups (Carter, R. W. and Geck, M., eds.), Cambridge University Press (1998), pp. 63–83.Google Scholar

Section 8

Kazhdan, D. and Lusztig, G., Representations of Coxeter groups and Hecke algebras, Inv. Math., 53 (1979), 165–184.CrossRefGoogle Scholar

Section 9

Kazhdan, D. and Lusztig, G., Schubert varieties and Poincaré duality, Proc. Symp. Pure Math. 36, Amer. Math. Soc. (1980), pp. 185–203.Google Scholar
Lusztig, G., Intersection cohomology methods in representation theory, Proc. Int. Congr. Math. Kyoto., Springer Verlag (1991), pp. 155–174.Google Scholar

Section 10

Beilinson, A., Bernstein, J. and Deligne, P., Faioceaux pervers, Analyse et topologie sur les éspaces singuliers (I), Astérisque 100, Paris, 1982.Google Scholar
Lusztig, G., Intersection cohomology complexes on a reductive group, Inv. Math., 75 (1984), 205–272.Google Scholar
Lusztig, G., Character sheaves I, Adv. in Math., 56 (1985), 193–237.Google Scholar
Lusztig, G., Character sheaves II, Adv. in Math., 57 (1985), 226–265.Google Scholar
Lusztig, G., Character sheaves III, Adv. in Math., 57 (1985), 266–315.Google Scholar
Lusztig, G., Character sheaves IV, Adv. in Math., 59 (1986), 1–63.Google Scholar
Lusztig, G., Character sheaves V, Adv. in Math., 61 (1986), 103–155.Google Scholar
Shoji, T., On the Green polynomials of classical groups, Invent. Math., 74 (1983), 239–264.Google Scholar
Shoji, T., Character sheaves and almost characters of reductive groups, Adv. in Math., 111 (1995), 244–313.Google Scholar
Shoji, T., Character sheaves and almost characters of reductive groups II, Adv. in Math., 111 (1995), 314–354.Google Scholar

Section 11

Beilinson, A. and Bernstein, J., Localisation de g-modules, C. R. Acad. Sci. Paris, Sér I. Math., 292 (1981), 15–18.Google Scholar
Brylinski, J.-L. and Kashiwara, M., Kazhdan-Lusztig conjecture and holonomic sys tems, Invent. Math., 64 (1981), 387–410.Google Scholar

Section 12

Lusztig, G. and Vogan, D., Singularities of closure of K-orbits on a flag manifold, Inv. Math., 71 (1983), 365–379.Google Scholar

Section 13, 14

Lusztig, G., Cuspidal local systems and graded Hecke algebras I, Publ. Math. IHES., 67 (1988), 145–202.Google Scholar
Lusztig, G., Cuspidal local systems and graded Hecke algebras II, Representations of Groups. Canad. Math. Soc. Conf. Proc. 16, Amer. Math. Soc. (1995), pp. 217–275.Google Scholar
Lusztig, G., Cuspidal local systems and graded Hecke algebras III, Representation Theory, 6 (2002), 202–242 (electronic).Google Scholar
Kazhdan, D. and Lusztig, G., Proof of the Deligne-Langlands conjecture for Hecke algebras, Inv. Math., 87 (1987), 153–215.Google Scholar
Lusztig, G., Equivariant K-theory and representations of Hecke algebras, Proc. Amer. Math. Soc., 94 (1985), 337–342.Google Scholar
Lusztig, G., Classification of unipotent representations of simple p-adic groups, Int. Math. Res. Notices, 1995, 517–589.CrossRefGoogle Scholar
Lusztig, G., Classification of unipotent representations of simple p-adic groups II, Representation Theory, 6 (2002), 243–289 (electronic).Google Scholar

Section 15

Lusztig, G., Quantum deformations of certain simple modules over enveloping algebras, Adv. in Math., 70 (1988), 237–249.Google Scholar
Lusztig, G., Quantum groups at roots of 1, Geom. Ded., 35 (1990), 89–114.Google Scholar
Kazhdan, D. and Lusztig, G., Affine Lie algebras and quantum groups, Int. Math. Res. Notices (1991), 21–29, In Duke Math. J., 62 (1991).Google Scholar
Kashiwara, M. and Tanisaki, T., Characters of the negative level highest weight modules for affine Lie algebras, Int. Math. Res. Notices, 3 (1994), 151–161.CrossRefGoogle Scholar

Section 16

Lusztig, G., Canonical bases arising from quantized enveloping algebras, J. Amer. Math. Soc., 3 (1990), 447–498.Google Scholar
Lusztig, G., Canonical bases arising from quantized enveloping algebras II, Common trends in mathematics and quantum field theories, Prog. of Theor. Phys. Suppl. 102 (1990), pp. 175–201.Google Scholar
Kashiwara, M., On crystal bases of the q-analogue of universal enveloping algebras, Duke Math. Jour., 63 (1991), 465–516.Google Scholar
Lusztig, G., Introduction to quantized enveloping algebras, Prog. in Math. 105, Birkhäuser (1992), pp. 49–65.Google Scholar

Section 17

Lusztig, G., Total positivity in reductive groups, Lie theory and geometry: in honor of B. Kostant, Prog. in Math. 123, Birkhäuser (1994), pp. 531–568.Google Scholar
Lusztig, G., Total positivity and canonical bases, Algebraic groups and Lie groups (Lehrer, G., ed.), Cambridge Univ. Press (1997), pp. 281–295.Google Scholar
Lusztig, G., Introduction to quantum groups, Prog. in Math. 110, Bikhäuser, 1993, 341 pp.Google Scholar

Section 18

Lusztig, G., Some problems in the representation theory of finite Chevalley groups, Proc. Symp. Pure Math. 37, Amer. Math. Soc. (1980), pp. 313–317.Google Scholar
Lusztig, G., Modular representations and quantum groups, Cotemp. Math., 82 (1989), 59–77.Google Scholar
Andersen, H. H., Jantzen, J. C. and Soergel, W., Representations of quantum groups at a pth root of unity and of semisimple groups in characteristic p: Independence of p, Astérisque 220, Paris, 1994.Google Scholar

Section 19

Lusztig, G., Representation theory in characteristic p, Taniguchi Conf. on Math. Nara 1998, Adv. Stud. Pure Math. 31 (2001), pp. 167–178.Google Scholar
Lusztig, G., Cells in affine Weyl groups I, Adv. Stud. Pure Math. 6 (1985), pp. 255–287.Google Scholar
Lusztig, G., Cells in affine Weyl groups II, J. Algebra, 109 (1987), 536–548.Google Scholar
Lusztig, G., Cells in affine Weyl groups III, J. Fac. Sci. Univ. Tokyo., 34 (1987), 223–243.Google Scholar
Lusztig, G., Cells in affine Weyl groups IV, J. Fac. Sci. Univ. Tokyo., 36 (1989), 297–328.Google Scholar
Bezrukavnikov, R., Mirkovic, I. and Rumynin, D., Localization of modules for a semisimple Lie algebra in prime characteristic, to appear, preprint, math.RT/0205144.Google Scholar