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.

Name thesis:degree_name

MSc

Level thesis:degree_level

Masters

Discipline thesis:degree_discipline

Sciences / Science

Grantor dc:publisher

Université d'Ottawa / University of Ottawa

Year dc:date.issued

2024

Author dc:creator

• Talarico, Marco

Advisor dc:contributor.supervisor

• Salmasian, Hadi

• Representation Theory
• Combinatorics
• Hecke Algebras

Language dc:language.iso

en

Identifier URI

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

Identifier

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

OAI record oai:identifier

https://ruor.uottawa.ca/server/oai/request?verb=GetRecord&metadataPrefix=dim&identifier=oai%3Aruor.uottawa.ca%3A10393%2F49979