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 semi-simple Lie algebras, and also for Capelli polynomial identities.
Recently I studied various probability measures on the so called Young graph. The Vershik-Kerovs 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
  Frobenius-Schur 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
  A-codimensions and A-cocharacters

Publications

1. A. Regev
• Asymptotics of Degrees of some S_n Regular Representations.
  Isr. J. Math., 113 (1999) 15-28.
2. A. Regev and A. Vershik
• Asymptotics of Young Diagrams and Hook Numbers.
  Electronic J. Combinatorics, 4 (1) (1997), \#R22.
3. A. Regev and D. Zeilberger
   • Proof of a Conjecture of Multisets of Hook Numbers.
     Ann. Combinatorics, 1 No. 4, (1997), 391--394.
4. A. Giambruno, A. Regev and M. Zaicev
   • On the Codimension Growth of Finite Dimensional Lie Algebras.
     J. Algebra, 220, (1999) 466-474.
5. S. Mishchenko, A. Regev and M. Zaicev
   • The Eponential Growth of Codimensions for Capelli Identities.
     Israel J. Math., 115 (2000) 333-342.
     
6. A. Regev
   • $S_\infty$ Representations and Combinatorial Identities.
     AMS Transactions, to appear.
     
7. A. Regev
   • Generalized Hook and Content Number Identities.
     Euro J. Comb., 21 no. 7, 949-957.
8. A. Regev
   • Generalized Hook and Content Number Identities - the Projective Case.
     Euro J. Comb., 21 no. 7, 959-966.
     
9. A. Berele and A. Regev
   • Exponential Growth of some P.I. Algebras.
     J. Algebra, to appear.
10. P. Cohen and A. Regev
    • A Six Generalized Square Theorem, with Applications to PI Algebras.
      J. Algebra, 239, 174-190 (2001).
11. G. Olshanski and A. Regev
    • Random Young Tableaux and Combinatorial Identities
      preprint.