
Professor Amitai Regev Tel: +97289344210 
The characters of the Symmetric groups S_{n} — 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 semisimple Lie algebras, and also for Capelli polynomial identities.
Recently I studied various probability measures on the so called Young graph. The VershikKerovs theory — and its extensions — relate these measures to 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.Preprints
 G. Olshanski, A. Regev and A. Vershik
FrobeniusSchur Functions
 G. Olshanski and A. Regev
Random Young Tableaux and Combinatorial Identities A. Regev
Double Centralizing Theorems for the Alternating Groups A. Henke and A. Regev
Weyl modules for the Schur Algebra of the Alternating Group A. Henke and A. Regev
Acodimensions and AcocharactersPublications
 A. Regev
 Asymptotics of Degrees of some S_{n }Regular Representations.
Isr. J. Math., 113 (1999) 1528. A. Regev and A. Vershik
 Asymptotics of Young Diagrams and Hook Numbers.
Electronic J. Combinatorics, 4 (1) (1997), \#R22. A. Regev and D. Zeilberger
 Proof of a Conjecture of Multisets of Hook Numbers.
Ann. Combinatorics, 1 No. 4, (1997), 391394. A. Giambruno, A. Regev and M. Zaicev
 On the Codimension Growth of Finite Dimensional Lie Algebras.
J. Algebra, 220, (1999) 466474. S. Mishchenko, A. Regev and M. Zaicev
 The Eponential Growth of Codimensions for Capelli Identities.
Israel J. Math., 115 (2000) 333342.
 A. Regev
 $S_\infty$ Representations and Combinatorial Identities.
AMS Transactions, to appear.
 A. Regev
 Generalized Hook and Content Number Identities.
Euro J. Comb., 21 no. 7, 949957. A. Regev
 Generalized Hook and Content Number Identities  the Projective Case.
Euro J. Comb., 21 no. 7, 959966.
 A. Berele and A. Regev
 Exponential Growth of some P.I. Algebras.
J. Algebra, to appear. P. Cohen and A. Regev
 A Six Generalized Square Theorem, with Applications to PI Algebras.
J. Algebra, 239, 174190 (2001). G. Olshanski and A. Regev
 Random Young Tableaux and Combinatorial Identities
preprint.
Faculty of Mathematics and Computer Science
Weizmann Institute of Science
Rehovot, 76100 Israel,
Tel: 97289343540 Fax: 97289344122
Email: math@wisdom.weizmann.ac.il