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prikaz prve stranice dokumenta Whittaker modules and fusion rules for the Weyl vertex algebra, affine vertex algebras and their orbifolds
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doctoral thesis
Whittaker modules and fusion rules for the Weyl vertex algebra, affine vertex algebras and their orbifolds
Zagreb: University of Zagreb, Faculty of Science, 2021. urn:nbn:hr:217:249471
Pedić Tomić, Veronika
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Pedić Tomić, V. (2021). Whittaker modules and fusion rules for the Weyl vertex algebra, affine vertex algebras and their orbifolds (Doctoral thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:249471

Pedić Tomić, Veronika. "Whittaker modules and fusion rules for the Weyl vertex algebra, affine vertex algebras and their orbifolds." Doctoral thesis, University of Zagreb, Faculty of Science, 2021. https://urn.nsk.hr/urn:nbn:hr:217:249471

Pedić Tomić, Veronika. "Whittaker modules and fusion rules for the Weyl vertex algebra, affine vertex algebras and their orbifolds." Doctoral thesis, University of Zagreb, Faculty of Science, 2021. https://urn.nsk.hr/urn:nbn:hr:217:249471

Pedić Tomić, V. (2021). 'Whittaker modules and fusion rules for the Weyl vertex algebra, affine vertex algebras and their orbifolds', Doctoral thesis, University of Zagreb, Faculty of Science, accessed 27 March 2025, https://urn.nsk.hr/urn:nbn:hr:217:249471

Pedić Tomić V. Whittaker modules and fusion rules for the Weyl vertex algebra, affine vertex algebras and their orbifolds [Doctoral thesis]. Zagreb: University of Zagreb, Faculty of Science; 2021 [cited 2025 March 27] Available at: https://urn.nsk.hr/urn:nbn:hr:217:249471

V. Pedić Tomić, "Whittaker modules and fusion rules for the Weyl vertex algebra, affine vertex algebras and their orbifolds", Doctoral thesis, University of Zagreb, Faculty of Science, Zagreb, 2021. Available at: https://urn.nsk.hr/urn:nbn:hr:217:249471

Metadata
TitleWhittaker modules and fusion rules for the Weyl vertex algebra, affine vertex algebras and their orbifolds
Title (croatian)Whittakerovi moduli i pravila fuzije za Weylovu verteks-algebru, afine verteks-algebre i njihove invarijantne podalgebre
AuthorVeronika Pedić Tomić
MentorDražen Adamović (mentor)
Committee memberOzren Perše (predsjednik povjerenstva)
Committee memberDražen Adamović (član povjerenstva)
Committee memberTomislav Šikić (član povjerenstva)
Committee memberSlaven Kožić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2021-07-13, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Universal decimal classification
(UDC)		51 - Mathematics
Abstract
The topic of this thesis are two problems in the vertex operator algebra theory: determination of fusion rules and the orbifold problem. For the fusion rules problem we study the example of Weyl vertex algebra, also known as the βγ ghost system. This is a nonrational vertex algebra, hence we give a first proof of a Verlinde formula for non-rational VOAs and confirm the Verlinde type conjecture given by D. Ridout and S. Wood in [70]. For the orbifold problem, we extend a theorem... More given in the Dong-Mason quantum Galois theory paper [41], from the category of ordinary modules to the whole category of weak modules. The proof given by Dong and Mason necessarily involves Zhu’s theory, and therefore cannot be extended to the category of weak modules. In particular, we study the example of Whittaker modules for the Weyl vertex algebra and Heisenberg VOA. In the first part of this thesis, we calculate fusion rules in the category of weight modules for the Weyl vertex algebra. Our proof is entirely vertex-algebraic and it uses the theory of intertwining operators for vertex algebras and the fusion rules for the affine vertex superalgebra L1((gl)(1|1)). Moreover, we explicitly construct the intertwining operators involved. We also prove a general irreducibility result which relates irreducible weight modules for the Weyl vertex algebra M to irreducible weight modules for L1((gl)(1|1)). In the second part of this thesis we prove a theorem on irreducible weak V-module W and an automorphism g of finite order. Here either W∘gi≆W for all i, in which case W is an irreducible V⟨g⟩–module, or W≅=W∘g in which case W is a direct sum of p irreducible V⟨g⟩–modules. The key idea of our proof was to consider a “big” module for the vertex algebra, constructed as a direct sum of modules ⨁iW∘gi. Moreover, we present a counterexample for the expansion of our theorem to the case of infinitedimensional group G for the irreducible Weyl algebra modules of Whittaker type. Less
Abstract (croatian)
U ovoj disertaciji proučavamo dvije teme teorije verteks-algebri: računanje pravila fuzije te problem podalgebre fiksnih točaka. Verteks-algebra za koju računamo pravila fuzije je Weylova verteks-algebra ili βγ sistem. To je iracionalna verteks-algebra i naš dokaz je prvi dokaz Verlindeove formule za slučaj iracionalnih verteks-algebri te potvrđujemo slutnju iznesenu u članku D. Ridouta i S. Wooda [70]. Za problem podalgebre fiksnih točaka proširujemo teorem C. Donga i G.... More Masona iz njihova članka o kvantnoj Galoisovoj teoriji [41], s kategorije jakih modula na cijelu kategoriju slabih modula. Dokaz iznesen u [41] ne može se proširiti na slabe module jer koristi Zhuovu teoriju. Svoj rezultat primjenjujemo na Weylovu verteks-algebru, ali i Heisenbergovu algebru verteks-operatora te za obje promatramo kategoriju Whittakerovih modula. U prvom dijelu disertacije računamo pravila fuzije u kategoriji težinskih modula Weylove verteks-algebre. Naš je dokaz potpuno uklopljen u teoriju verteks-algebri te koristi teoriju operatora ispreplitanja verteks-algebri i pravila fuzije za afinu verteks-superalgebru L1((gl)(1|1)). Štoviše, eksplicitno smo konstruirali operatore ispreplitanja koji se javljaju u iskazu. Također, pokazali smo općeniti rezultat koji povezuje ireducibilne težinske module Weylove verteks-algebre M s ireducibilnim težinskim modulima za L1((gl)(1|1)). U drugom dijelu disertacije dokazali smo teorem o ireducibilnim slabim V–modulima W i automorfizmu g konačnog reda. Naime, pokazali smo da je ili W∘gi≆W, za sve i, i u tom slučaju je W ireducibilan V⟨g⟩–modul, ili je W≅=W∘g, i u tom slučaju je W direktna suma p ireducibilnih V⟨g⟩–modula. Glavna ideja našeg dokaza je bila konstruirati “veliki” ˇ modul za verteks-algebru, tako da uzmemo direktnu sumu modula ⨁iW∘gi. Nadalje, dajemo protuprimjer za proširenje našeg teorema na slučaj beskonačno-dimenzionalne grupe automorfizama G za ireducibilne Whittakerove module Weylove verteks-algebre. Less
Keywords
Keywords (croatian)
Languageenglish
URN:NBNurn:nbn:hr:217:249471
Promotion2022
Study programmeTitle: 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 resourceText
Extentviii, 91 str.
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2022-01-24 12:12:23
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