Download the fullsized PDF
Share
Permanent link (DOI): https://doi.org/10.7939/R35D8NP3V
Communities
This file is in the following communities:
Graduate Studies and Research, Faculty of 
Collections
This file is in the following collections:
Theses and Dissertations 
Finitedimensional representations of Yangians Open Access
Descriptions
 Other title
 Subject/Keyword

Cyclicity conditions
Local Weyl modules
Yangians
 Type of item
 Thesis
 Degree grantor

University of Alberta
 Author or creator

Tan, Yilan
 Supervisor and department

Guay, Nicolas (Math)
 Examining committee member and department

Guay, Nicolas (Math)
Adrega De Moura, Adriano (Math)
Kuttler, Jochen (Math)
Cliff, Gerald (Math)
Pianzola, Arturo (Math)
 Department

Department of Mathematical and Statistical Sciences
 Specialization

Mathematics
 Date accepted

20140924T10:03:05Z
 Graduation date

201411
 Degree

Doctor of Philosophy
 Degree level

Doctoral
 Abstract

In this thesis, we study local Weyl modules of Yangians and a cyclicity condition for a tensor product of fundamental representations of a Yangian. Let $\g$ be a simple Lie algebra over $\C$ with rank $l$ and $\pi$ be a generic $l$tuple of polynomials in $u$. We show that there exists a universal representation $W(\pi)$ of the Yangian $\yg$, called the local Weyl module associated to $\pi$, such that every finitedimensional highestweight representation associated to $\pi$ is a quotient of $W(\pi)$. We prove that the dimension of $W(\pi)$ is bounded by the dimension of some local Weyl module of the current algebra $\g[t]$. Let $L=V_{a_1}(\omega_{b_1})\otimes V_{a_2}(\omega_{b_2})\otimes\ldots\otimes V_{a_k}(\omega_{b_k})$, where $V_{a_i}(\omega_{b_i})$ is the $b_i$th fundamental representation of $\yg$. We prove that if $\operatorname{Re}(a_1)\geq\operatorname{Re}(a_2)\geq \ldots \geq \operatorname{Re}(a_k)$, then $L$ is a highest weight representation. By comparing the dimensions of $L$ and the upper bound of $W(\pi)$, we have $W(\pi)\cong L$. A cyclicity condition of the tensor product $L$ is also studied: $L$ is a highest weight representation if $a_ja_i\notin S(b_i, b_j)$ for $1\leq i
 Language

English
 DOI

doi:10.7939/R35D8NP3V
 Rights
 This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for the purpose of private, scholarly or scientific research. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
 Citation for previous publication

File Details
 Date Uploaded
 20140917T17:36:24.342+00:00
 Date Modified
 20141115T08:17:26.216+00:00
 Audit Status
 Audits have not yet been run on this file.
 Characterization

File format: pdf (Portable Document Format)
Mime type: application/pdf
File size: 1445474
Last modified: 2016:08:04 02:41:0606:00
Filename: Tan_Yilan_201409_PhD.pdf
Original checksum: 3c60b715c91dd297135964f47734d005
Well formed: true
Valid: true
Status message: Too many fonts to report; some fonts omitted. Total fonts = 1721
File title: Background
Page count: 145
User Activity  Date 
