Decomposition numbers for symmetric groups
ثبت نشده
چکیده
Where to find decomposition matrices? Try www.math.rwth-aachen.de/∼MOC In hard copy, [6] has several (at the end) for small primes. For p = 2, a paper by Juergen Mueller(Aachen) [7], for an electronic version try his homepage. General background can be found in [6]. Column removal: Due to G.D. James, sometime after '76. Just now I cannot find the precise reference. However, a generalization of the various removals has recently been done by Fayers and Lyle [3]. A reference to the original should be in there. Two-part partitions: The original paper is [5], it is just for p = 2. The odd prime paper is slightly later (again, I cannot find the reference just now). But there is not much in it, he just says 'it's the same as p = 2. His proof is quite long. There is now a short proof, due to S. Donkin, using new technology. This can be found in [1], the last chapter. More on fractal structure of decomposition matrices for 2-part partitions can be found in [4]. Blocks. The result by Scopes (including details with the abacus) is in [8]. The decomposition map: The details are in the paper [2]. to be added reference for the number of simples in a p-block of weight w. Maybe in [8] there is a reference? References [1] K. Erdmann, Symmetric groups and quasi-hereditary algebras. in Finite dimensional algebras and related topics, ed V.
منابع مشابه
DECOMPOSITION METHOD FOR SOLVING FULLY FUZZY LINEAR SYSTEMS
In this paper, we investigate the existence of a positive solution of fully fuzzy linear equation systems. This paper mainly to discuss a new decomposition of a nonsingular fuzzy matrix, the symmetric times triangular (ST) decomposition. By this decomposition, every nonsingular fuzzy matrix can be represented as a product of a fuzzy symmetric matrix S and a fuzzy triangular matrix T.
متن کاملOn the Orbits of Collineation Groups
1. Introduction In this paper we consider some results on the orbits of groups of collineations, or, more generally, on the point and block classes of tactical decompositions, on symmetric balanced incomplete block designs (symmetric BIBD = (v, k, 2)-system=finite 2-plane), and we consider generalizations to (not necessarily symmetric) BIBD and other combinatorial designs. The results are about...
متن کاملThe tilting tensor product theorem and decomposition numbers for symmetric groups
We show how the tilting tensor product theorem for algebraic groups implies a reduction formula for decomposition numbers of the symmetric group. We use this to prove generalisations of various theorems of Erdmann and of James and Williams. Let G be a semisimple, connected, simply-connected algebraic group over an algebraically closed field k of characteristic p > 0. The simple modules L(λ) are...
متن کاملJames’s Conjecture holds for weight four blocks of Iwahori–Hecke algebras
James’s Conjecture suggests that in certain cases, the decomposition numbers for the Iwahori– Hecke algebra of the symmetric group over a field of prime characteristic (and in particular, the decomposition numbers for the symmetric group itself) coincide with the decomposition numbers for a corresponding Iwahori–Hecke algebra defined over C, and hence can be computed using the LLT algorithm. We...
متن کاملRepresentation Theory of Symmetric Groups and Related Hecke Algebras
We survey some fundamental trends in representation theory of symmetric groups and related objects which became apparent in the last fifteen years. The emphasis is on connections with Lie theory via categorification. We present results on branching rules and crystal graphs, decomposition numbers and canonical bases, graded representation theory, connections with cyclotomic and affine Hecke alge...
متن کاملFoulkes Modules and Decomposition Numbers of the Symmetric Group
The decomposition matrix of a finite group in prime characteristic p records the multiplicities of its p-modular irreducible representations as composition factors of the reductions modulo p of its irreducible representations in characteristic zero. The main theorem of this paper gives a combinatorial description of certain columns of the decomposition matrices of symmetric groups in odd prime ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009