arXiv math/01070542001-07math.QAmath.CO

Bosonic formulas for (k,l)-admissible partitions

B. Feigin, M. Jimbo, S. Loktev, T. Miwa, E. Mukhin

备注：: Latex, 29 pages

英文摘要：

Bosonic formulas for generating series of partitions with certain restrictions are obtained by solving a set of linear matrix q-difference equations. Some particular cases are related to combinatorial problems arising from solvable lattice models, representation theory and conformal field theory.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Addendum to `Bosonic formulas for $(k,l)$-admissible partitions'

In our earlier paper we made a combinatorial study of (k,l)-admissible partitions. This object appeared already in the work of M. Primc as a label of a basis of level k-integrable modules over $\hat{sl}_l$. We clarify the relation between these two works. As a byproduct we obtain an explicit parameterization of the affine Weyl group of $\hat{sl}_l$ by a simple combinatorial set.

2001-12-11math.COmath.QAmath.RT

Vertex Operators of Admissible Modules of $U_q(C^{(1)}_n)$

Using our recent bosonic realization of $U_q(\widehat{sp}_{2n})$, we construct explicitly the vertex operators for the level -1/2 modules of $U_q(\widehat{sp}_{2n})$ using bosonic fields. Our method contains a detailed analysis of all the q-intertwining relations.

1997-01-28math.QAq-alg

The Genus Two Partition Function for Free Bosonic and Lattice Vertex Operator Algebras

We define the $n$-point function for a vertex operator algebra on a genus two Riemann surface in two separate sewing schemes where either two tori are sewn together or a handle is sewn to one torus. We explicitly obtain closed formulas for the genus two partition function for the Heisenberg free bosonic string and lattice vertex operator algebras in both sewing schemes. We prove that the partition functions are holomorphic in the sewing parameters on given suitable domains and describe their modular properties. Finally, we show that the partition functions cannot be equal in the neighborhood o…

2007-12-04hep-thmath.NTmath.QA

Bosonization of Admissible Representations of $U_q(\widehat{sl}_2)$ at Level $-\frac{1}{2}$ and $q$-Vertex Operators

We construct a representation of $U_q(\widehat{sl}_2)$ at level $-1/2$ by using the bosonic Fock spaces. The irreducible modules are obtained as the kernel of a certain operator, in contrast to the construction by Feingold and Frenkel for $q=1$ where such a procedure is not necessary. We also bosonize the $q$-vertex operators associated with the vector representation.

1996-05-20math.QAq-alg

Free Bosonic Vertex Operator Algebras on Genus Two Riemann Surfaces II

We continue our program to define and study $n$-point correlation functions for a vertex operator algebra $V$ on a higher genus compact Riemann surface obtained by sewing surfaces of lower genus. Here we consider Riemann surfaces of genus 2 obtained by attaching a handle to a torus. We obtain closed formulas for the genus two partition function for free bosonic theories and lattice vertex operator algebras $V_L$. We prove that the partition function is holomorphic in the sewing parameters on a given suitable domain and describe its modular properties. We also compute the genus two Heisenberg v…

2011-11-09math.QA

Free Bosonic Vertex Operator Algebras on Genus Two Riemann Surfaces I

We define the partition and $n$-point functions for a vertex operator algebra on a genus two Riemann surface formed by sewing two tori together. We obtain closed formulas for the genus two partition function for the Heisenberg free bosonic string and for any pair of simple Heisenberg modules. We prove that the partition function is holomorphic in the sewing parameters on a given suitable domain and describe its modular properties for the Heisenberg and lattice vertex operator algebras and a continuous orbifolding of the rank two fermion vertex operator super algebra. We compute the genus two H…

2009-12-01hep-thmath.NTmath.QA

更多相关论文收起更多论文

Genus Two Meromorphic Conformal Field Theory

We construct the genus two (or two loop) partition function for meromorphic bosonic conformal field theories. We use a sewing procedure involving two genus one tori by exploiting an explicit relationship between the genus two period matrix and pinching modular parameters. We obtain expressions for the partition function for the chiral bosonic string, even rank lattice theories and self-dual meromorphic conformal field theories including the Moonshine Module. In particular, we find that for self-dual theories with central charge 24, the genus two partition function multiplied by a universal hol…

2000-03-09hep-thmath.NTmath.QA