28 research outputs found
Cells and Constructible Representations in type B
We examine the partition of a finite Coxeter group of type into cells
determined by a weight function . The main objective of these notes is to
reconcile Lusztig's description of constructible representations in this
setting with conjectured combinatorial descriptions of cells.Comment: 15 pages, 5 figure
Knuth Relations for the Hyperoctahedral Groups
C. Bonnaf{\'e}, M. Geck, L. Iancu, and T. Lam have conjectured a description
of one-sided cells in unequal parameter Hecke algebras of type which is
based on domino tableaux of arbitrary rank. In the integer case, this
generalizes the work of D. Garfinkle whose methods we adapt to construct a
family of operators which generate the conjectured combinatorial description.Comment: 23 page
On the classification of primitive ideals for complex classical Lie algebras, IV
This paper is the fourth and last in the series "On the classification of
primitive ideals for complex classical Lie algebras", extending earlier results
in other classical types to type D. The generalized tau-invariant used in
earlier work must now be defined in a different way, using a family of
operators attached to a quadruple of simple roots spanning a subsystem of type
D_4. each taking one or two values. Using these operators we show that
primitive ideals of trivial infinitesimal character are characterized by their
generalized tau-invariants and are parametrized by standard domino tableaux of
the appropriate special shape.Comment: 32 page