Maximal and Primitive Elements in Weyl Modules for TypeA2
نویسندگان
چکیده
منابع مشابه
Fully Commutative Elements in the Weyl and Affine Weyl Groups
Let W be a Weyl or affine Weyl group and let Wc be the set of fully commutative elements in W . We associate each w ∈ Wc to a digraph G(w). By using G(w), we give a graph-theoretic description for Lusztig’s a-function on Wc and describe explicitly all the distinguished involutions of W . The results verify two conjectures in our case: one was proposed by myself in [15, Conjecture 8.10] and the ...
متن کاملSubmodules of Specht Modules for Weyl Groups
The construction of all irreducible modules of the symmetric groups over an arbitrary field which reduce to Specht modules in the case of fields of characteristic zero is given by G.D.James. Halıcıoğlu and Morris describe a possible extension of James’ work for Weyl groups in general, where Young tableaux are interpreted in terms of root systems. In this paper we show how to construct submodule...
متن کاملPeriodicity of Weyl Modules for SL(2,9)
Weyl modules play a central role in the representation theory of the general and special linear groups. There has been great interest recently in the modular case of these groups over fields of prime characteristic p. In particular, Glover [l] has proved some remarkable and comprehensive results about these modules for SL(2,p). We shall extend one of these theorems to the case of SL(2, q) where...
متن کاملWeyl Modules for the Twisted Loop Algebras
The notion of a Weyl module, previously defined for the untwisted affine algebras, is extended here to the twisted affine algebras. We describe an identification of the Weyl modules for the twisted affine algebras with suitably chosen Weyl modules for the untwisted affine algebras. This identification allows us to use known results in the untwisted case to compute the dimensions and characters ...
متن کاملPrimitive Elements
Importantly, there is no element 1 ≤ k < p − 1 such that a ≡ 1(modp). The concepts presented in the study of primitive elements can be considered special cases of more general idea presented in group theory. Specifically, the primitve element a can be seen as a generator of Zp, we wil discuss this in more detail in the first section of the paper. Primitive elements also have applications in enc...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1999
ISSN: 0021-8693
DOI: 10.1006/jabr.1998.7766