منابع مشابه
Web bases for the general linear groups
Let V be the representation of the quantized enveloping algebra of gl(n) which is the q-analogue of the vector representation and let V ∗ be the dual representation. We construct a basis for ⊗r (V ⊕ V ∗) with favorable properties similar to those of Lusztig’s dual canonical basis. In particular our basis is invariant under the bar involution and contains a basis for the subspace of invariant te...
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We prove two results. (1) There is an absolute constant D such that for any finite quasisimple group S, given 2D arbitrary automorphisms of S, every element of S is equal to a product of D ‘twisted commutators’ defined by the given automorphisms. (2) Given a natural number q, there exist C = C(q) and M = M(q) such that: if S is a finite quasisimple group with |S/Z(S)| > C, βj (j = 1, . . . ,M) ...
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We prove that every quasisimple group of classical type is a product of boundedly many conjugates of a quasisimple subgroup of type An. 1 Main Result and Notation Let S be a quasisimple group of classical Lie type X , that is one from {An, Bn, Cn, Dn, An, Dn}. Its classical definition is as a quotient of some group of linear transformations of a vector space over a finite field F preserving a n...
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We study the problem of removing an element from an additive basis in a general abelian group. We introduce analogues of the classical functions X,S and E (defined in the case of N) and obtain bounds on them. Our estimates on the functions SG and EG are valid for general abelian groups G while in the case of XG we show that distinct types of behaviours may occur depending on G.
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Bases, determining sets, metric dimension, . . . The notion of a base, and various combinatorial variants on it, have been rediscovered many times in different parts of combinatorics, especially graph theory: base size has been called fixing number, determining number, rigidity index, etc. Robert Bailey and I have written a survey paper attempting to describe all these and related concepts and ...
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ژورنال
عنوان ژورنال: Algebra & Number Theory
سال: 2018
ISSN: 1944-7833,1937-0652
DOI: 10.2140/ant.2018.12.1537