nLab George Lusztig

George Lusztig; is a mathematician at MIT, born in Romania. He has many deep contributions to Lie theory and representation theory, especially using and developing the methods of geometric representation theory. He discovered the canonical bases of quantum and Lie groups (in a sense dual to the crystal basis of Masaki Kashiwara).

• $n$Lab: Kazhdan-Lusztig theory
• homepage
• list of papers and his own comments on some papers
• wikipedia

Selected works

• George Lusztig, Intersection cohomology methods in representation theory, Proc. ICM 1990, pdf

Kazhdan-Lusztig theory:

• David Kazhdan, George Lusztig, Representations of Coxeter groups and Hecke algebras, Invent. Math. 53:2 (1979) 165–184, MR81j:20066, doi

On total positivity in the context of reductive groups

• George Lusztig, Total positivity in reductive groups. In: Brylinski, JL., Brylinski, R., Guillemin, V., Kac, V. (eds) Lie Theory and Geometry. Progress in Mathematics 123; Birkhäuser 1994 doi

On quantum groups (and relations to quivers and canonical bases)

• George Lusztig, Quivers, perverse sheaves, and quantized enveloping algebras J. Amer. Math. Soc., 4(2):365–421 (1991)
• George Lusztig, Canonical bases arising from quantized enveloping algebras, J. Am. Math. Soc. 3 (2), 447–498 (1990) doi
• George Lusztig, Canonical bases in tensor products. Proc. Natl. Acad. Sci. 89 (1992) 8177–8179 doi
• G. Lusztig, Quivers, perverse sheaves, and quantized enveloping algebras, J. Amer. Math. Soc. 4(2), 365–421 (1991)
• G. Lusztig, Introduction to Quantum Groups, Birkhauser (1992)
• G. Lusztig, Canonical bases and Hall algebras, In: Representation Theories and Algebraic Geometry (Montreal, PQ, 1997), 365–399, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 514. Kluwer (1998)

On Kazhdan-Luzstig correspondence and monoidal structures

• George Lusztig, David Kazhdan, Tensor structures arising from affine Lie algebras, J. Amer. Math. Soc. 6 (1993) 905-947 doi, Part II: J. Amer. Math. Soc. (1993), 949-1011 doi; Part III: J. Amer. Math. Soc. (1994) 335-381 doi; Part IV: J. Amer. Math. Soc. (1994) 383-453 doi.
• G. Lusztig, Comments on my papers, arXiv:1707.09368, 55 pages, contains historical notes on some of Lusztig’s papers and the list of 247 publications till mid 2017

category: people