• A
• A
• A
• ABC
• ABC
• ABC
• А
• А
• А
• А
• А
Regular version of the site

# Geometric Interpretation of the Integrable Crystals via Generalized Slices

Student: Vasily Krylov

Supervisor:

Faculty: Faculty of Mathematics

Educational Programme: Mathematics (Bachelor)

Let $G$ be a connected reductive algebraic group over $\BC$. Let $\Lap_{G}$ be the lattice of dominant coweights of $G$. It is known (see \cite{Jo}) that if $G$ is of adjoint type then there is a unique family of crystals of highest weight $\bB(\la)$ such that for every $\la_{1}, \la_{2} \in \Lap_{G}$ there exists the map of crystals $\bp_{\la_{1},\la_{2}}: \bB(\la_{1}) \otimes \bB(\la_{2}) \ra \bB(\la_{1}+\la_{2})\cup\{0\}.$ In the first part of the paper we construct crystals $\bB(\la)$ using the geometry of generalized transversal slices. After that we construct the maps $\bp_{\la_{1},\la_{2}}$ in terms of multiplication of generalized transversal slices. Let $L \subset G$ be a Levi subgroup inside $G$. In the third part of the paper we describe the restriction functor $\on{Res}^{\check{G}}_{\check{L}}$ using hyperbolic restriction functors between different subvarieties in generalized transversal slices.

Full text (added June 10, 2017)

Student Theses at HSE must be completed in accordance with the University Rules and regulations specified by each educational programme.

Summaries of all theses must be published and made freely available on the HSE website.

The full text of a thesis can be published in open access on the HSE website only if the authoring student (copyright holder) agrees, or, if the thesis was written by a team of students, if all the co-authors (copyright holders) agree. After a thesis is published on the HSE website, it obtains the status of an online publication.

Student theses are objects of copyright and their use is subject to limitations in accordance with the Russian Federation’s law on intellectual property.

In the event that a thesis is quoted or otherwise used, reference to the author’s name and the source of quotation is required.