Modules for order preserving symplectic and even special orthogonal rook monoids

Modules for order preserving symplectic and even special orthogonal rook monoids We study two classes of modules for order preserving symplectic and order preserving even special orthogonal rook monoids. The first class of modules are indexed by admissible sets, and the second are the regular representations. For the first class we show that every submodule is cyclic and completely reducible, and for each irreducible component when restricted to a module over a proper submonoid we explore its module properties. For the second we provide explicitly their decompositions into irreducible submodules using admissible sets. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Semigroup Forum Springer Journals

Modules for order preserving symplectic and even special orthogonal rook monoids

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Publisher
Springer US
Copyright
Copyright © 2017 by Springer Science+Business Media, LLC
Subject
Mathematics; Algebra
ISSN
0037-1912
eISSN
1432-2137
D.O.I.
10.1007/s00233-017-9887-0
Publisher site
See Article on Publisher Site

Abstract

We study two classes of modules for order preserving symplectic and order preserving even special orthogonal rook monoids. The first class of modules are indexed by admissible sets, and the second are the regular representations. For the first class we show that every submodule is cyclic and completely reducible, and for each irreducible component when restricted to a module over a proper submonoid we explore its module properties. For the second we provide explicitly their decompositions into irreducible submodules using admissible sets.

Journal

Semigroup ForumSpringer Journals

Published: Jul 5, 2017

References

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