Fermionic expressions for minimal model Virasoro characters / / Trevor A. Welsh

• Record Nr.: UNINA9910818805703321
• Autore: Welsh Trevor A (Trevor Alan), <1963->
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , [2005]; ©2005
• ISBN: 1-4704-0428-1
• Descrizione fisica: 1 online resource (176 p.)
• Collana: Memoirs of the American Mathematical Society, , 0065-9266 ; ; number 827
• Classificazione: 31.30
• Disciplina: 510 s; 511/.62
• Soggetti: Combinatorial enumeration problems; Lie algebras
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "Volume 175, number 827 (third of 4 numbers)."
• Nota di bibliografia: Includes bibliographical references (pages 159-160).
• Nota di contenuto: ""Contents""; ""1. Prologue""; ""1.1. Introduction""; ""1.2. Structure of this paper""; ""1.3. Continued fractions""; ""1.4. Fermionic character expressions""; ""1.5. The Takahashi and string lengths""; ""1.6. Takahashi trees""; ""1.7. Takahashi tree vectors""; ""1.8. Truncated Takahashi tree""; ""1.9. The linear term""; ""1.10. The constant term""; ""1.11. The quadratic term""; ""1.12. The mn-system and the parity vector""; ""1.13. The extra term""; ""1.14. Finitized fermionic expressions""; ""1.15. Fermionic-like expressions""; ""2. Path combinatorics""; ""2.1. Outline of proof""; ""2.2. The band structure""""2.3. Weighting function""; ""2.4. Winged generating functions""; ""2.5. Striking sequence of a path""; ""2.6. Path parameters""; ""2.7. Scoring generating functions""; ""2.8. A seed""; ""2.9. Partitions""; ""3. The B-transform""; ""3.1. Path-dilation: the B[sub(1)]-transform""; ""3.2. Particle insertion: the B[sub(2)]-transform""; ""3.3. Particle moves""; ""3.4. The B[sub(3)]-transform""; ""3.5. Particle content of a path""; ""4. The D-transform""; ""4.1. The pure D-transform""; ""4.2. The BD-pair""; ""5. Mazy runs""; ""5.1. The passing sequence""; ""5.2. The passing function""""5.3. Transforming the passing function""; ""5.4. Mazy runs in the original weighting""; ""6. Extending and ; truncating paths""; ""6.1. Extending paths""; ""6.2. Truncating paths""; ""7. Generating the fermionic expressions""; ""7.1. Runs and the core result""; ""7.2. Induction parameters""; ""7.3. The induction""; ""7.4. Transferring to the original weighting""; ""7.5. The other direction""; ""7.6. The mn-system""; ""8. Collating the runs""; ""8.1. Pulling the drawstrings""; ""8.2. Constraints of the Takahashi tree""; ""8.3. Gathering in the Takahashi tree""