Higher Specht Polynomials for Representations of Iwahori-Hecke Algebras

In this thesis we construct a generalization of the higher Specht polynomials to the Hecke algebra 𝓗_𝑞(𝑆_𝑛). These polynomials form a basis of the coinvariant algebra 𝕮 with respect to the action of 𝑆_𝑛, and they will decompose 𝕮 into irreducible representations of the Hecke algebra. These irreducible representations are 𝑞-Specht modules 𝑆_λ^𝑞. In this construction, if we consider 𝑞 = 1 then we obtain the original higher Specht polynomials for 𝑆_𝑛. We will also introduce a generalization of the divided difference and Demazure operators in the setting of the ring of Laurent polynomials 𝔏. We will construct a coinvariant algebra for the action of the hyperoctahedral group 𝑊_𝑛 on 𝔏. From these operators, we will be able to find a faithful representation of the Hecke algebra 𝓗_{𝑞,𝑝}(𝑊_𝑛) over 𝔏.

Grantor dc:publisher

Université d'Ottawa / University of Ottawa

Year dc:date

2024

Author dc:creator

• Talarico, Marco

Contributors dc:contributor

• Salmasian, Hadi

• Representation Theory
• Combinatorics
• Hecke Algebras

Language dc:language

en

Identifier

https://doi.org/10.20381/ruor-30783

OAI identifier oai:identifier

oai:ruor.uottawa.ca:10393/49979