Fermionic expressions for minimal model Virasoro characters
著者
書誌事項
Fermionic expressions for minimal model Virasoro characters
（Memoirs of the American Mathematical Society, no. 827）
American Mathematical Society, c2005
大学図書館所蔵 件 / 全16件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
"Volume 175, number 827 (third of 4 numbers)."
Includes bibliographical references (p.159-160)
内容説明・目次
内容説明
Fermionic expressions for all minimal model Virasoro characters $\chi^{p,p'}_{r,s}$ are stated and proved. Each such expression is a sum of terms of fundamental fermionic form type. In most cases, all these terms are written down using certain trees which are constructed for $s$ and $r$ from the Takahashi lengths and truncated Takahashi lengths associated with the continued fraction of $p'//p$. In the remaining cases, in addition to such terms, the fermionic expression for $\chi^{p,p'}_{r,s}$ contains a different character $\chi^{\hat p, \hat p'}_{\hat r, \hat s}$, and is thus recursive in nature. Bosonic-fermionic $q$-series identities for all characters $\chi^{p,p'}_{r,s}$ result from equating these fermionic expressions with known bosonic expressions. In the cases for which $p=2r$, $p=3r$, $p'=2s$ or $p'=3s$, Rogers-Ramanujan type identities result from equating these fermionic expressions with known product expressions for $\chi^{p,p'}_{r,s}$.The fermionic expressions are proved by first obtaining fermionic expressions for the generating functions $\chi^{p,p'}_{a, b, c}(L)$ of length $L$ Forrester-Baxter paths, using various combinatorial transforms. In the $L\to\infty$ limit, the fermionic expressions for $\chi^{p,p'}_{r,s}$ emerge after mapping between the trees that are constructed for $b$ and $r$ from the Takahashi and truncated Takahashi lengths respectively.
目次
Prologue Path combinatorics The $\mathcal{B}$-transform The $\mathcal{D}$-transform Mazy runs Extending and truncating paths Generating the fermionic expressions Collating the runs Fermionic character expressions Discussion Appendix A. Examples Appendix B. Obtaining the bosonic generating function Appendix C. Bands and the floor function Appendix D. Bands on the move Appendix E. Combinatorics of the Takahashi lengths Bibliography.
「Nielsen BookData」 より