2026-09-19T16:56:08Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1448472022-08-30T03:32:40Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Etingof, Pavel
Utiralova, Aleksandra
Massachusetts Institute of Technology. Department of Mathematics
2022-08-29T16:15:55Z
2022-08-29T16:15:55Z
2022-05
2022-08-16T16:40:21.626Z
https://hdl.handle.net/1721.1/144847
In this work we study Harish-Chandra bimodules in the setting of the Deligne categories Rep(Gₜ). We classify all pairs (χ, ψ) of central characters of U(gₜ) for which there exists a non-zero Harish-Chandra bimodule over gₜ, such that the two copies of the center Z(U(gₜ)) act via characters χ and ψ. Thus, we answer Question 3.25 posed in Pavel Etingof’s paper Representation Theory in Complex Rank II.
We also construct a family of Harish-Chandra bimodules that interpolate simple finite dimensional bimodules in the classical case. It turns out that they have finite K-type, which is a non-vacuous condition for the Harish-Chandra bimodules in Rep(Gₜ). The full classification of (simple) finite K-type bimodules is yet unknown.
This construction also yields some examples of central characters χ of the universal enveloping algebra U(gₜ) for which the quotient Uₓ is not simple, and, thereby, it allows us to partially solve Problem 3.23 posed in Representation Theory in Complex Rank II.
Ph.D.
Massachusetts Institute of Technology
In Copyright - Educational Use Permitted
Copyright MIT
http://rightsstatements.org/page/InC-EDU/1.0/
Harish-Chandra Bimodules in Complex Rank
Thesis
application/pdf
Doctoral
Doctor of Philosophy
Publication
unknown
unknown
<Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="89a8bad9-c185-474b-abc6-54a2dc91b058">
<Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type>
<Title>Harish-Chandra Bimodules in Complex Rank</Title>
<PublishedIn>
<Publication>
</Publication>
</PublishedIn>
<PublicationDate>2022-05</PublicationDate>
<Authors>
<Author>
<DisplayName>Utiralova, Aleksandra</DisplayName>
<Affiliation>
<OrgUnit>
</OrgUnit>
</Affiliation>
</Author>
</Authors>
<Editors>
</Editors>
<Publishers>
<Publisher>
<DisplayName>Massachusetts Institute of Technology</DisplayName>
<OrgUnit />
</Publisher>
</Publishers>
<License>http://rightsstatements.org/page/InC-EDU/1.0/</License>
<Abstract>In this work we study Harish-Chandra bimodules in the setting of the Deligne categories Rep(Gₜ). We classify all pairs (χ, ψ) of central characters of U(gₜ) for which there exists a non-zero Harish-Chandra bimodule over gₜ, such that the two copies of the center Z(U(gₜ)) act via characters χ and ψ. Thus, we answer Question 3.25 posed in Pavel Etingof’s paper Representation Theory in Complex Rank II.
We also construct a family of Harish-Chandra bimodules that interpolate simple finite dimensional bimodules in the classical case. It turns out that they have finite K-type, which is a non-vacuous condition for the Harish-Chandra bimodules in Rep(Gₜ). The full classification of (simple) finite K-type bimodules is yet unknown.
This construction also yields some examples of central characters χ of the universal enveloping algebra U(gₜ) for which the quotient Uₓ is not simple, and, thereby, it allows us to partially solve Problem 3.23 posed in Representation Theory in Complex Rank II.</Abstract>
<Access xmlns="http://purl.org/coar/access_right"
>
</Access>
</Publication>