Amitai Regev
The Herman P. Taubman Professor of Mathematics
Ring Theory:
The characters of the Symmetric groups Sn —
and their degrees — provide a powerful tool in the quantitative study of the polynomial
identities satisfied by non commutative algebras, both associative and non associative.
The description of the related asymptotic invariants was recently obtained for
semi-simple Lie algebras, and also for Capelli polynomial identities.
Representation Theory:
A variant of I. Schur's double-centralizing theorem was proved — for the actions
of the the alternating group An on an n-fold
tensor product V⊗ n of a vector space
V. The corresponding Weyl modules, in the Z2 graded case, were
studied.
Combinatorics:
Recently I studied various probability measures on the so called Young graph.
The VK (Vershik-Kerov) theory — and its extensions — relate these measures
with the character theory on S∞, the infinite symmetric group. Combined with
some formulas from the theory of symmetric functions, the study of these probability
measures yields (infinitely) many new combinatorial and hypergeometric identities.
The study of various permutation-statistics on the symmetric groups and on related groups — continues. New refinements and extensions of MacMahon's classical equi-distribution theorem are found, relating that sub-area of Enumerative-Combinatorics to the sub-area of Shape-Avoiding-Permutations.
Recent Publications
- Double centralizing theorems for the alternating groups. J. Algebra 250 (2002) 335-352.
- [with A. Henke] Weyl modules for the Schur algebra of the Alternating group. J. Algebra 257 (1) (2002) 169-196.
- [with Y. Roichman] Permutation statistics on the alternating group, to appear in the Adv. App. Math. (arXiv: CO/0302301).