The Symplectic Monoid |
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| Authors: | You'an Cao Jie Lei Zhenheng Li |
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| Institution: | 1. Department of Mathematics , Xiangtan University , Xiangtan , Hunan , P.R. China cya@xtu.edu.cn;3. Department of Mathematics , Xiangtan University , Xiangtan , Hunan , P.R. China;4. Department of Mathematical Sciences , University of South Carolina Aiken , Aiken , SC , USA |
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| Abstract: | In this paper, we describe explicitly the symplectic monoid ? and its Renner monoid ? using elementary methods. We refine the Bruhat–Renner decomposition of ? and analyze in detail the length function on ?. We then show that every element of ? has a unique canonical form decomposition, which is an analogue of the canonical form of elements in Chevalley groups. We also compute the order of ? over a finite field, and as a consequence we obtain a new combinatorial identity. |
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| Keywords: | Bruhat decomposition Length function Renner monoid Symplectic monoid Weyl group |
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