Year: 2008
Type: preprint
Abstract: We show four formulas for calculating the orders of finite reductive monoids with zero. As applications, these formulas are then used to calculate the orders of finite reductive monoids induced from the $F_q$-split $\J$-irreducible monoids $\overline {K^*ρ(G_0)}$ where $G_0$ is a simple algebraic group over the algebraic closure of $F_q$, and $ρ: G_0\to GL(V)$ is the irreducible representation associated with any dominant weight. Finally, we give an explicit formula for the orders of finite symplectic monoids associated with the last fundamental dominant weight of type $C_l$; the connections to $H$-polynomials and Betti numbers are shown.
Source: arXiv (Cornell University)
Authors: Li, Zhuo, Li, Zhenheng, Cao, You'an
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1634594032