Hecke monoids, their homomorphisms and parabolicity

Summary · qwen2.5:32b

The study explores homomorphisms in Hecke monoids, focusing on the properties and classification of parabolic and injective homomorphisms, revealing a rich structure of parabolic homomorphisms and classifying locally injective connected homomorphisms between classical types, which unexpectedly provides insight into all homomorphisms between Hecke monoids.

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An interesting exploration of Hecke monoids and their homomorphisms. If you're into maths, this might pique your interest!

Excerpt

arXiv:2605.09761v2 Announce Type: replace Abstract: We study homomorphisms of Hecke monoids, notably parabolic homomorphisms, which map parabolic elements to parabolic elements, and injective ones. The importance of the first class stems from the fact that parabolic elements form a rather mysterious submonoid of the Hecke monoid, and we found a plethora of parabolic homomorphisms. Concerning injective ones, as a first step towards their classification, we classified all locally injective connected homomorphisms between Hecke monoids of classical types and expect all of them to be injective. As a surprising byproduct of our study of parabolic and injective homomorphisms we described, to some extent, all homomorphisms between Hecke monoids.