Modules for order preserving symplectic and even special orthogonal rook monoids

作者：Liu, Wenli^*; Bai, Ximei; Feng, Jianqiang; Bai, Ruipu

来源：Semigroup Forum, 2018, 96(3): 417-437.

DOI：10.1007/s00233-017-9887-0

• Rook monoid
• Order preserving
• Symplectic rook monoid
• Orthogonal rook monoid
• Irreducible module

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.

• 出版日期2018-6
• 单位河北大学