nLab Andrei Zelevinsky

Andrei Zelevinsky has main interests in representation theory, algebraic geometry, polyhedral and algebraic combinatorics and Lie theory (not in the sense as in $n$lab, but in the common sense of the circle of questions relating Lie algebras, Lie groups, Kac-Moody groups, quantum groups etc.). With Sergey Fomin, he created a theory of cluster algebras. He studied multidimensional generalizations of hypergeometric functions, arrangements of hyperplanes, bases for quantum groups, quantum determinants and minors, Grassmanians, flag and Schubert varieties etc.

• I. M. Gelfand, M. M. Kapranov, A. Zelevinsky, Discriminants, resultants, and multidimensional determinants, Birkhäuser 1994, 523 pp.

• Sergey Fomin, Andrei Zelevinsky, Cluster algebras. I. Foundations, J. Amer. Math. Soc. 15 (2002) no. 2, 497–529 math.RT/0104151; Cluster algebras. II. Finite type classifications. Invent. Math. 154 (2003) no. 1, 63–121 – classification of cluster algebras of finite type via root systems math.RA/0208229.

• Arkady Berenstein, Andrei Zelevinsky, Quantum cluster algebras, math.QA/0404446

• A. Zelevinsky’s homepage

category: people