Branching from the general linear group to the symmetric group and the principal embedding

บทความในวารสาร

ผู้เขียน/บรรณาธิการ

กลุ่มสาขาการวิจัยเชิงกลยุทธ์

รายละเอียดสำหรับงานพิมพ์

รายชื่อผู้แต่ง: Heaton A., Sriwongsa S., Willenbring J.F.

ปีที่เผยแพร่ (ค.ศ.): 2021

Volume number: 4

Issue number: 2

หน้าแรก: 189

หน้าสุดท้าย: 200

จำนวนหน้า: 12

eISSN: 2589-5486

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85105343587&doi=10.5802%2fALCO.138&partnerID=40&md5=7ab152bc42c08de13a3db25a8b8c3279

ภาษา: English-Great Britain (EN-GB)

ดูบนเว็บไซต์ของสำนักพิมพ์

บทคัดย่อ

Let S be a principally embedded sl2-subalgebra in sln for n > 3. A special case of results of the third author and Gregg Zuckerman implies that there exists a positive integer b(n) such that for any finite-dimensional irreducible sln-representation, V , there exists an irreducible S-representation embedding in V with dimension at most b(n). In a 2017 paper (joint with Hassan Lhou), they prove that b(n) = n is the sharpest possible bound, and also address embeddings other than the principal one. These results concerning embeddings may be interpreted as statements about plethysm. Then, in turn, a well known result about these plethysms can be interpreted as a “branching rule”. Specifically, a finite dimensional irreducible representation of GL(n, C) will decompose into irreducible representations of the symmetric group when it is restricted to the subgroup consisting of permutation matrices. The question of which irreducible representations of the symmetric group occur with positive multiplicity is the topic of this paper, applying the previous work of Lhou, Zuckerman, and the third author. © The journal and the authors, 2021.

คำสำคัญ

Branching, Howe duality, Plethysm, Principal embedding