-Carter partitions, their crystal-theoretic behavior and generating function.
A class of projective representations of hyperoctahedral groups and Schur Q-functions
A combinatorial formula for orthogonal idempotents in the 0-Hecke algebra of the symmetric group.
A family of critically finite maps with symmetry.
The symmetric group Sn acts as a reflection group on CPn-2 (for n>=3).Associated with each of the (n2) transpositions in Sn is an involution on CPn-2 that pointwise fixes a hyperplane -the mirrors of the action. For each such action, there is a unique Sn-symmetric holomorphic map of degree n+1 whose critical set is precisely the collection of hyperplanes. Since the map preserves each reflecting hyperplane, the members of this family are critically-finite in a very strong sense. Considerations...
A generating function for fatgraphs
A geometric version of the Kerov-Kirillov-Reshetikhin construction. (Une version géométrique de la construction de Kerov-Kirilov-Reshetikhin.)
A one-box-shift morphism between Specht modules.
A remark on the irreducible characters and fake degrees of finite real reflection groups.
A semigroup approach to wreath-product extensions of Solomon's descent algebras.
A stability property for coefficients in Kronecker products of complex characters.
A theorem on restricted group representations.
A Theorem on the Restriction of Group Characters, and Its Application to the Character Theory of SL (n, q).
An algorithm for the decomposition of ideals of the group ring of a symmetric group.
Applications de Gauss et pléthysme
Les représentations irréductibles de sont décrites par les foncteurs de Schur, dont la composition définit le pléthysme. Sa compréhension est un problème important en théorie des invariants, ou bien en relation avec les représentations des groupes symétriques.Nous proposons dans cet article une approche géométrique du problème. Généralisant les plongements classiques de Veronese et de Segre, nous construisons des plongements de variétés de drapeaux dans d’autres variétés de drapeaux, sur lesquels...
Artin's conjecture, Turing's method, and the Riemann hypothesis.
Asymptotic Behaviour of Colength of Varieties of Lie Algebras
This project was partially supported by RFBR, grants 99-01-00233, 98-01-01020 and 00-15-96128.We study the asymptotic behaviour of numerical characteristics of polynomial identities of Lie algebras over a field of characteristic 0. In particular we investigate the colength for the cocharacters of polynilpotent varieties of Lie algebras. We prove that there exist polynilpotent Lie varieties with exponential and overexponential colength growth. We give the exact asymptotics for the colength of a product...
Bethe Ansatz and the geography of rigged strings
We demonstrate the way in which composition of two famous combinatorial bijections, of Robinson-Schensted and Kerov-Kirillov-Reshetikhin, applied to the Heisenberg model of magnetic ring with spin 1/2, defines the geography of rigged strings (which label exact eigenfunctions of the Bethe Ansatz) on the classical configuration space (the set of all positions of the system of r reversed spins). We point out that each l-string originates, in the language of this bijection, from an island of l consecutive...
Bilinear forms for SL(2,q), An and similar groups.
The set of invariant symmetric bilinear forms on irreducible modules over fields of characteristic zero for certain groups is studied. Results are obtained under the presence in a finite group of elements of order four whose square is central. In particular, we find that the relevant modules for the groups mentioned in the title always accept an invariant symmetric bilinear form under which the module admits an orthonormal basis.
Blocks and Defect Groups of Monomial Groups.
Blocks for symmetric groups and their covering groups and quadratic forms.