On the Equivariant K -theory of the Nilpotent Cone in the General Linear Group

Corrections To: “on the Equivariant K -theory of the Nilpotent Cone in the General Linear Group”

In the paper [P. Achar, On the equivariant K-theory of the nilpotent cone in the general linear group, Represent. Theory 8 (2004), 180–211], the author gave a combinatorial algorithm for computing the Lusztig–Vogan bijection for GL(n,C). However, that paper failed to mention one easy case that may sometimes arise, making the description of the algorithm incomplete. This note fills in that gap.

On the Equivariant K-theory of the Nilpotent Cone

In this note we construct a “Kazhdan-Lusztig type” basis in equivariant K-theory of the nilpotent cone of a simple algebraic group G. This basis conjecturally is very close to the basis of this K-group consisting of irreducible bundles on nilpotent orbits. As a consequence we get a natural (conjectural) construction of Lusztig’s bijection between dominant weights and pairs {nilpotent orbit O, i...

Equivariant Coherent Sheaves on the Nilpotent Cone in the General Linear Group

On the Exponent of Triple Tensor Product of p-Groups

The non-abelian tensor product of groups which has its origins in algebraic K-theory as well as inhomotopy theory, was introduced by Brown and Loday in 1987. Group theoretical aspects of non-abelian tensor products have been studied extensively. In particular, some studies focused on the relationship between the exponent of a group and exponent of its tensor square. On the other hand, com...

Modular generalized Springer correspondence I: the general linear group

We define a generalized Springer correspondence for the group GL(n) over any field. We also determine the cuspidal pairs, and compute the correspondence explicitly. Finally we define a stratification of the category of equivariant perverse sheaves on the nilpotent cone of GL(n) satisfying the ‘recollement’ properties, and with subquotients equivalent to categories of representations of a produc...