Teorija reprezentacija hermitskih kvaternionskih grupa nad p-adskim poljima

doctoral thesis

• Title (english): Representation theory of hermitian quaternionic groups over p-adic fields
• Author: Nevena Jurčević Peček
• Mentor: Neven Grbac (mentor)
• Mentor: Marcela Hanzer (komentor)
• Committee member: Goran Muić (predsjednik povjerenstva)
• Committee member: Marcela Hanzer (član povjerenstva)
• Committee member: Ivan Matić (član povjerenstva)
• Committee member: Neven Grbac (član povjerenstva)
• Committee member: Marko Tadić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2016-01-25, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics
• Universal decimal classification (UDC): 51 - Mathematics

Abstract

U ovoj disertaciji proučavamo problem reducibilnosti reprezentacija p-adskih hermitskih kvaternionskih grupa koje su parabolički inducirane iz kuspidalnih i (esencijalno) kvadratno integrabilnih reprezentacija Levijevih faktora standardnih paraboličkih podgrupa. Glavni rezultati su generalizacija Tadićevih kriterija reducibilnosti za rascjepive simplektičke i neparne specijalne ortogonalne grupe na slučaj proizvoljnih hermitskih kvaternionskih grupa. Dokazi se baziraju na tehnikama Jacquetovih modula te koriste strukturnu formulu i teoriju R-grupa. Pritom je pokazano da za hermitske kvaternionske grupe vrijedi strukturna formula te su određene R-grupe.

Abstract (english)

In the thesis, the reducibility of representations of p-adic hermitian quaternionic groups that are parabolically induced from cuspidal and (essentially) square-integrable representations of the Levi factors of standard parabolic subgroups is studied. Main results generalize the reducibility criteria of Tadi´c for split symplectic and special orthogonal groups to the case of arbitrary hermitian quaternionic groups. Proofs rely on the Jacquet module techniques and use the structure formula and the theory of R-groups. It is proved that for Hermitian quaternionic groups the structure formula holds and the R-groups are determined.

• Keywords: hermitske kvaternionske grupe; parabolički inducirane reprezentacije; Jacquetovi moduli; R-grupa; reducibilnost; strukturna formula; p-adsko polje; klasične grupe
• Keywords (english): hermitian quaternionic groups; parabolically induced representations; Jacquet modules; R-groups; reducibility; structure formula; p−adic fields; classical groups
• Language: croatian
• URN:NBN: urn:nbn:hr:217:993618
• Study programme: Title: Mathematics; Study programme type: university; Study level: postgraduate; Academic / professional title: doktor/doktorica znanosti, područje prirodnih znanosti, polje matematika (doktor/doktorica znanosti, područje prirodnih znanosti, polje matematika)
• Type of resource: Text
• Extent: vii, 107 str.
• File origin: Born digital
• Access conditions: Closed access
• Created on: 2019-03-08 13:20:27