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A decomposition of the descent algebra of the hyperoctahedral group, II

✍ Scribed by Nantel Bergeron

Publisher
Elsevier Science
Year
1992
Tongue
English
Weight
1000 KB
Volume
148
Category
Article
ISSN
0021-8693

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Here we give an interpretation of Solomon's rule for multiplication in the descent algebra of Coxeter groups of type D, ⌺ D . We describe an ideal I I such n that ⌺ D rI I is isomorphic to the descent algebra of the hyperoctahedral group, n ⌺ B .

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Let A be a finite-dimensional hereditary algebra over a finite field, and let Ž . Ž . H H A and C C A be, respectively, the Ringel᎐Hall algebra and the composition w x Ž . w x algebra of A. Define r to be the element Ý M g H H A , where M runs over d the isomorphism classes of the regular A-modules