Showing papers on "Modular representation theory published in 1996"
TL;DR: In this article, the representation ring of the quantum double of a finite group over fields of arbitrary characteristic is decompositions into ideals involving Green rings of subgroups and given characters of such Green rings, all characters arise in this fashion.
93 citations
23 citations
TL;DR: In this paper, it was shown that for an irreducible subvariety of 3kr−1 and a cyclic shifted subgroup, the direct sum decomposition of the subgroup is the same upon restriction, and moreover, this decomposition is completely determined by the behavior of the restriction to the cyclic shift subgroup corresponding to the generic point of the point.
13 citations
TL;DR: In modular representation theory, a standard question is: What is the Zr p -dimension of the Z r p -vector space Ext K, K? as mentioned in this paper, which is called intertwining number.
12 citations
TL;DR: In modular representation theory of a finite group, the theory of Green vertices plays an important role as mentioned in this paper and Harish-Chandra induction has become one of the most important tools in the last decades.
11 citations
TL;DR: In this paper, the cohomological Brauer group of a real algebraic variety is calculated for Enriques surfaces. But this method cannot be used to determine the Brauer groups of real algebraian surfaces.
Abstract: Methods are developed for calculating the cohomological Brauer group of a real algebraic variety, and they are used to determine completely the Brauer group of an Enriques surface.
8 citations
1 Nov 1996
TL;DR: In this paper, it was shown that finitely generated modules can have infinitely generated summands, and that including these summands in the category repairs the lack of Krull-Schmidt property.
Abstract: In the modular representation theory of finite groups, much recent effort has gone into describing cohomological properties of the category of finitely generated modules. In recent joint work of the author with Jon Carlson and Jeremy Rickard[ 3 ], it has become clear that for some purposes the finiteness restriction is undesirable. In particular, in the quotient category of kG -modules by the subcategory of modules of less than maximal complexity, it turns out that finitely generated modules can have infinitely generated summands, and that including these summands in the category repairs the lack of Krull–Schmidt property.
3 citations
1 Jan 1996
1 Feb 1996
TL;DR: In this article, the modular representation theory of the general linear group GLn in the defining characteristic p > 0 has been studied and several results relating to the modular representations of simple modules in symmetric powers of the natural module, or in tensor products of truncated symmetric power are obtained.
Abstract: Several results are obtained relating to the modular representation theory of the general linear group GLn in the defining characteristic p > 0. In Section 1, embeddings of certain simple modules in symmetric powers of the natural module, or in tensor products of truncated symmetric powers, are constructed. In Section 2, cases are found where simple quotientsof Schur modules H0(λ) can be constructed by extending theidea of truncation to these modules in a natural way. In Section 3, the characters of those simple modules which can be constructed as twisted tensor products of truncated symmetric powers are expressed in terms of Schur functions.