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- W4289294731 abstract "For an arbitrary finite monoid $M$ and subgroup $K$ of the unit group of $M$, we prove that there is a bijection between irreducible representations of $M$ with nontrivial $K$-fixed space and irreducible representations of $mathcal{H}_K$, the convolution algebra of $Ktimes K$-invariant functions from $M$ to $F$, where $F$ is a field of characteristic not dividing $|K|$. When $M$ is reductive and $K = B$ is a Borel subgroup of the group of units, this indirectly provides a connection between irreducible representations of $M$ and those of $F[R]$, where $R$ is the Renner monoid of $M$. We conclude with a quick proof of Frobenius Reciprocity for monoids for reference in future papers." @default.
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- W4289294731 date "2018-11-10" @default.
- W4289294731 modified "2023-10-17" @default.
- W4289294731 title "Convolution Algebras for Finite Reductive Monoids" @default.
- W4289294731 doi "https://doi.org/10.48550/arxiv.1811.04334" @default.
- W4289294731 hasPublicationYear "2018" @default.
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