منابع مشابه
1 4 Ju n 20 02 Ramified Partition Algebras
For each natural number n, poset T , and |T |–tuple of scalars Q, we introduce the ramified partition algebra P (T) n (Q), which is a physically motivated and natural generalization of the partition algebra [24, 25] (the partition algebra coincides with case |T | = 1). For fixed n and T these algebras, like the partition algebra, have a basis independent of Q. We investigate their representatio...
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where the LGLn(λ) are irreducible GLn(C)-modules and the S λ k are irreducible Sk-modules. The decomposition in (0.1) essentially makes the study of the representations of GLn(C) and the study of representations of the symmetric group Sk two sides of the same coin. The group GLn(C) has interesting subgroups, GLn(C) ⊇ On(C) ⊇ Sn ⊇ Sn−1, and corresponding centralizer algebras, CSk ⊆ CBk(n) ⊆ CAk(...
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A family of quantum cluster algebras is introduced and studied. In general, these algebras are new, but sub-classes have been studied previously by other authors. The algebras are indexed by double partitions or double flag varieties. Equivalently, they are indexed by broken lines L. By grouping together neighboring mutations into quantum line mutations we can mutate from the cluster algebra of...
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In this paper we study the representation theory of two partition algebras related to complex reflection groups. The colored partition algebras, Pk(n, r) introduced by Bloss [2] and the algebras, Tk(n, r) introduced by Tanabe [26]. In particular, we describe the decomposition of these algebras in terms of irreducible representations.
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The permutation representation theory of groups has been extended, through quasigroups, to one-sided left (or right) quasigroups. The current paper establishes a link with the theory of ordered sets, introducing the concept of a Burnside order that generalizes the poset of conjugacy classes of subgroups of a finite group. Use of the Burnside order leads to a simplification in the proof of key p...
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ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2004
ISSN: 0025-5874,1432-1823
DOI: 10.1007/s00209-003-0581-4