Let R be the homogeneous coordinate ring of Grassmannian G=Gr(2,n) defined over an algebraically closed field k characteristic p≥max⁡{n−2,3}. In this paper we give a description decomposition R, considered as graded Rpr-module, for r≥2. This is companion to [16], where case r=1 was treated, and taken together, our results imply that has finite F-representation type (FFRT). Though it expected al...

We study multiplicity free representations of connected reductive groups. First we give a simple criterion to decide the multiplicity freeness of a representation. Then we determine all invariant differential operators in terms of a finite reflection group, the little Weyl group, and give a characterization of the spectrum of the Capelli operators. At the end, we reproduce the classification of...

The representation theory of reductive groups, such as the group GLn of invertible complex matrices, is an important topic, with applications to number theory, algebraic geometry, mathematical physics, and quantum topology. One way to study this representation theory is through the geometric Satake correspondence (also known as geometric Langlands duality). This correspondence relates the geome...

Let G be a split reductive algebraic group over a non-archimedean local field. We study the representation theory of a central extension G̃ of G by a cyclic group of order n, under some mild tameness assumptions on n. In particular, we focus our attention on the development of the theory of principal series representations for G̃ and its applications to the study of Hecke algebras via a Satake is...

the freiheitssatz of magnus for one-relator groups is one of the cornerstones of combinatorial group theory. in this short note which is mostly expository we discuss the relationship between the freiheitssatz and corre-sponding results in free power series rings over fields. these are related to results of schneerson not readily available in english. this relationship uses a faithful representa...

In the winter of 1999 I gave a series of lectures at Queen’s university about some recent results concerning the Cohen-Macaulay property of invariants of Hopf algebras. Tony Geramita asked me to write up my notes for the Queen’s Papers, and I happily took up his suggestion. Although this article focuses on the proof of one main theorem (Theorem 2.11 on page 12), it has some of the character of ...

In the late 1960s, Robert Langlands proposed a new and far-reaching connection between the representation theory of Lie groups over real and -adic fields, and the structure of the Galois groups of these fields [24]. Even though this local Langlands correspondence remains largely conjectural, the relation that it predicts between representation theory and number theory has profoundly changed our...

We develop a theory of microlocalization for Harish-Chandra modules, adapting construction Losev [Duke Math. J. 159 (2011), pp. 99–143]. explore the applications this to unipotent representations real reductive groups. For representation complex group, we deduce formula restriction maximal compact subgroup, proving an old conjecture Vogan [Associated varieities and representations</ital...

Abstract In analogy with the Barbasch–Vogan duality for real reductive linear groups, we introduce a notion useful representation theory of metaplectic groups. This is map on set nilpotent orbits in complex symplectic Lie algebra, whose range consists so-called special orbits. We relate this primitive ideals and extend unipotent representations to also interpret terms double cells Weyl group re...