Abstract
In this paper, we give a general formula for a Renner monoid of a reductive monoid with zero. It is based on Putcha's type map. We apply this formula to find the orders of the Renner monoids for J -irreducible monoids K ∗ ρ ( G ) ¯ where G is a simple algebraic group over an algebraically closed field K, and ρ : G → GL ( V ) is an irreducible representation associated with an arbitrary fundamental dominant weight.
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