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The Partition Algebras and a New Deformation of the Schur Algebras

✍ Scribed by P Martin; D Woodcock


Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
371 KB
Volume
203
Category
Article
ISSN
0021-8693

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πŸ“œ SIMILAR VOLUMES


The Structure of the Partition Algebras
✍ Paul Martin πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 353 KB

Γ„ 4 1 1 2 2 3 3 4 4 5 5 Ε½ ÄÄ 4 as clusters, and of composition of partitions ab s Q. ␣ , ␣ , ␣ , ␣ , 1 2 3 4 Γ„ 4 Γ„ 4 Γ„ 4 4 . Ε½ ␣ , ␀ , ␀ , ␀ , ␀ , ␀ by an appropriate juxtaposition cf. p. 868 5 1 2 3 4 5 w x. of 2 . We define the elements of S , Ä␣ , ␀ 4 n Γ„ 4 Γ„ 4 Γ„ 4 Γ„ 4

The Blocks of theq-Schur Algebra
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In [8], Scopes verified the Donovan conjecture for blocks of the finite symmetric groups. Her main theorem ( 1.3 below) was proved by finding a sufficient condition for Morita equivalence between two blocks of the same weight. Since there is a close connection between representations of the symmetri

Schur Algebras and Global Bases: New Pro
✍ D. Woodcock πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 463 KB

Let U be the quantised enveloping algebra associated to a finite-type w x w x root datum, as defined by Drinfeld 10 and Jimbo 17 , and modified by w x w y1 x Ε½ . Lusztig 24 . Put A A s β€«ήšβ€¬ q, q . In the first instance U is a ‫ޑ‬ q -algebra; by analogy with the Kostant ‫-ήšβ€¬form of the classical envel

The Global Dimension of Schur Algebras f
✍ Alison E Parker πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 255 KB

We first define the notion of good filtration dimension and Weyl filtration dimension in a quasi-hereditary algebra. We calculate these dimensions explicitly for all irreducible modules in SL and SL . We use these to show that the global 2 3 dimension of a Schur algebra for GL and GL is twice the go