D-Index & Metrics Best Publications

George Lusztig

MIT
United States

D-Index & Metrics D-index (Discipline H-index) only includes papers and citation values for an examined discipline in contrast to General H-index which accounts for publications across all disciplines.

Discipline name Citations Publications World Ranking National Ranking

Mathematics D-index 68 Citations 25,973 305 World Ranking 221 National Ranking 123

Research.com Recognitions

Awards & Achievements

2013 - Fellow of the American Mathematical Society

2008 - Steele Prize for Lifetime Achievement

1999 - Brouwer Medal

1992 - Member of the National Academy of Sciences

1991 - Fellow of the American Academy of Arts and Sciences

1985 - Frank Nelson Cole Prize in Algebra

1983 - Fellow of the Royal Society, United Kingdom

1982 - Fellow of John Simon Guggenheim Memorial Foundation

Overview

What is he best known for?

The fields of study George Lusztig is best known for:

Tensor product
Lie algebra
Lie group

His research brings together the fields of Unipotent and Pure mathematics. His Algebra over a field study frequently draws connections between adjacent fields such as Affine Lie algebra. George Lusztig performs integrative study on Affine Lie algebra and Lie algebra in his works. He undertakes interdisciplinary study in the fields of Lie algebra and Current algebra through his research. His studies link Algebra over a field with Current algebra. His Affine transformation study often links to related topics such as Geometry. His Geometry study frequently draws parallels with other fields, such as Affine transformation. George Lusztig combines Quantum mechanics and Quantum in his research. He incorporates Quantum and Quantum mechanics in his studies.

His most cited work include:

Canonical bases arising from quantized enveloping algebras (974 citations)
Representations of Reductive Groups Over Finite Fields (632 citations)
Quantum deformations of certain simple modules over enveloping algebras (446 citations)

What are the main themes of his work throughout his whole career to date

His Geometry study frequently draws connections between related disciplines such as Character (mathematics). George Lusztig regularly ties together related areas like Geometry in his Character (mathematics) studies. He integrates Quantum mechanics and Pure mathematics in his studies. George Lusztig combines Mathematical analysis and Pure mathematics in his studies. His work on Reductive group is being expanded to include thematically relevant topics such as Group theory. His work in Group theory is not limited to one particular discipline; it also encompasses Reductive group.

George Lusztig most often published in these fields:

Pure mathematics (85.23%)
Algebra over a field (57.95%)
Geometry (23.86%)

What were the highlights of his more recent work (between 2012-2019)?

Pure mathematics (85.71%)
Algebra over a field (57.14%)
Group (periodic table) (42.86%)

In recent works George Lusztig was focusing on the following fields of study:

His research on Pure mathematics frequently links to adjacent areas such as Invertible matrix. Algebra over a field is closely attributed to Pure mathematics in his research. His work in Group (periodic table) is not limited to one particular discipline; it also encompasses Quantum mechanics. His Quantum mechanics study often links to related topics such as Group (periodic table). His Cell biology study frequently links to related topics such as Non canonical. His research brings together the fields of Cell biology and Non canonical. Combinatorics is closely attributed to Finite field in his research. As part of his studies on Finite field, he often connects relevant areas like Combinatorics. His Reductive group study frequently draws connections between related disciplines such as Algebraic number.

Between 2012 and 2019, his most popular works were:

Total Positivity in Reductive Groups (211 citations)
Canonical Bases Arising from Quantized Enveloping Algebras. II (105 citations)
Special representations of Weyl groups: A positivity property (12 citations)

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Best Publications

Introduction to Quantum Groups

George Lusztig.
(1993)

3212 Citations

Representations of Coxeter Groups and Hecke Algebras.

David Kazhdan;George Lusztig.
Inventiones Mathematicae (1979)

2450 Citations

Canonical bases arising from quantized enveloping algebras

G. Lusztig.
Journal of the American Mathematical Society (1990)

1740 Citations

Affine Hecke algebras and their graded version

George Lusztig.
Journal of the American Mathematical Society (1989)

1000 Citations

Representations of reductive groups over finite fields

Pierre Deligne;G. Lusztig.
Annals of Mathematics (1976)

943 Citations

Characters of reductive groups over a finite field

George Lusztig.
(1984)

746 Citations

Representations of reductive groups over finite fields

P. Deligne;G. Lusztig.
Annals of Mathematics (1976)

738 Citations

Quantum deformations of certain simple modules over enveloping algebras

G Lusztig.
Advances in Mathematics (1988)

735 Citations

Quivers, perverse sheaves, and quantized enveloping algebras

G. Lusztig.
Journal of the American Mathematical Society (1991)

707 Citations

Proof of the Deligne-Langlands conjecture for Hecke algebras

David Kazhdan;George Lusztig.
Inventiones Mathematicae (1987)

689 Citations

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Frequent Co-Authors

External Links

Personal Website for George Lusztig