7 research outputs found
Fermionic expressions for minimal model Virasoro characters
Fermionic expressions for all minimal model Virasoro characters 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 and from the
Takahashi lengths and truncated Takahashi lengths associated with the continued
fraction of . In the remaining cases, in addition to such terms, the
fermionic expression for contains a different character
, and is thus recursive in nature.
Bosonic-fermionic -series identities for all characters result from equating these fermionic expressions with known bosonic
expressions. In the cases for which , , or ,
Rogers-Ramanujan type identities result from equating these fermionic
expressions with known product expressions for .
The fermionic expressions are proved by first obtaining fermionic expressions
for the generating functions of length
Forrester-Baxter paths, using various combinatorial transforms. In the
limit, the fermionic expressions for emerge
after mapping between the trees that are constructed for and from the
Takahashi and truncated Takahashi lengths respectively.Comment: 153 pages, includes eps figures. v2: exceptional cases clarified,
(1.45/6) corrected for d=1, Section 7.5 rewritten, reference added. v3: minor
typos and clarifications. To appear in Memoirs of the American Mathematical
Societ