منابع مشابه
Standard Monomials and Extremal Vector Systems
We say that a set system F ⊆ 2 shatters a given set S ⊆ [n] if 2 = {F ∩ S : F ∈ F}. The Sauer-Shelah lemma states that in general, a set system F shatters at least |F| sets. A set system is called shattering-extremal if it shatters exactly |F| sets. In [9] and [13] an algebraic characterization of shattering-extremal set systems was given, which offered the possibility to generalize the notion ...
متن کاملCanonical Bases and Standard Monomials
Let U be the quantized enveloping algebra associated to a simple Lie algebra g by Drinfel’d and Jimbo. Let λ be a classical fundamental weight for g, and V (λ) the irreducible, finite-dimensional type 1 highest weight U -module with highest weight λ. We show that the canonical basis for V (λ) (see Kashiwara [6, §0] and Lusztig [18, 14.4.12]) and the standard monomial basis (see [11, §§2.4 & 2.5...
متن کاملYoung Diagrams, Standard Monomials and Invariant Theory
The topics I want to treat have various sources: (1) the fundamental theorems of invariant theory of the classical groups, (2) the representation theory of classical groups, (3) the geometry of the Grassmann and flag varieties. The initial interest in these questions came for me from the solution given by Formanek and myself, [8], of Mumford's conjecture for the linear group, [25], obtained ind...
متن کاملStandard monomials for wonderful group compactifications
Let X be the wonderful compactification of the semisimple adjoint algebraic group G. We show that the basis of H0(X,L) constructed in [CM03] is compatible with all B×B-orbit closures in X by defining subsets using only combinatorics of the underlying paths. Furthermore, we construct standard monomials on X that have properties similar to classical standard monomials.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2020
ISSN: 0012-365X
DOI: 10.1016/j.disc.2019.111785