### Abstract

The spaces of coinvariants are quotient spaces of integrable s-fractur sign and l-fractur sign_{2} modules by subspaces generated by the actions of certain subalgebras labeled by a set of points on a complex line. When all the points are distinct, the spaces of coinvariants essentially coincide with the spaces of conformai blocks in the WZW conformal field theory and their dimensions are given by the Verlinde rule. We describe monomial bases for the s-fractur sign and l-fractur sign_{2} spaces of coinvariants, In particular, we prove that the spaces of coinvariants have the same dimensions when all the points coincide. We establish recurrence relations satisfied by the monomial bases and the corresponding characters of the spaces of coinvariants. For the proof we use filtrations of the s-fractur sign and l-fractur sign _{2} modules. The adjoint graded spaces are certain modules on the loop Heisenberg algebra. The recurrence relation is established by using filtrations on these modules.

Original language | English (US) |
---|---|

Pages (from-to) | 419-474 |

Number of pages | 56 |

Journal | Selecta Mathematica, New Series |

Volume | 8 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 2002 |

Externally published | Yes |

### Fingerprint

### Keywords

- Affine Lie algebra
- Combinatorics
- Conformal field theory

### ASJC Scopus subject areas

- Mathematics(all)
- Physics and Astronomy(all)

### Cite this

_{2}spaces of coinvariants: Loop Heisenberg modules and recursion.

*Selecta Mathematica, New Series*,

*8*(3), 419-474. https://doi.org/10.1007/s00029-002-8112-4

**Combinatorics of the s-fractur sign and l-fractur sign _{2} spaces of coinvariants : Loop Heisenberg modules and recursion.** / Feigin, B.; Kedem, Rinat; Loktev, S.; Miwa, T.; Mukhin, E.

Research output: Contribution to journal › Article

_{2}spaces of coinvariants: Loop Heisenberg modules and recursion',

*Selecta Mathematica, New Series*, vol. 8, no. 3, pp. 419-474. https://doi.org/10.1007/s00029-002-8112-4

_{2}spaces of coinvariants: Loop Heisenberg modules and recursion. Selecta Mathematica, New Series. 2002 Jan 1;8(3):419-474. https://doi.org/10.1007/s00029-002-8112-4

}

TY - JOUR

T1 - Combinatorics of the s-fractur sign and l-fractur sign2 spaces of coinvariants

T2 - Loop Heisenberg modules and recursion

AU - Feigin, B.

AU - Kedem, Rinat

AU - Loktev, S.

AU - Miwa, T.

AU - Mukhin, E.

PY - 2002/1/1

Y1 - 2002/1/1

N2 - The spaces of coinvariants are quotient spaces of integrable s-fractur sign and l-fractur sign2 modules by subspaces generated by the actions of certain subalgebras labeled by a set of points on a complex line. When all the points are distinct, the spaces of coinvariants essentially coincide with the spaces of conformai blocks in the WZW conformal field theory and their dimensions are given by the Verlinde rule. We describe monomial bases for the s-fractur sign and l-fractur sign2 spaces of coinvariants, In particular, we prove that the spaces of coinvariants have the same dimensions when all the points coincide. We establish recurrence relations satisfied by the monomial bases and the corresponding characters of the spaces of coinvariants. For the proof we use filtrations of the s-fractur sign and l-fractur sign 2 modules. The adjoint graded spaces are certain modules on the loop Heisenberg algebra. The recurrence relation is established by using filtrations on these modules.

AB - The spaces of coinvariants are quotient spaces of integrable s-fractur sign and l-fractur sign2 modules by subspaces generated by the actions of certain subalgebras labeled by a set of points on a complex line. When all the points are distinct, the spaces of coinvariants essentially coincide with the spaces of conformai blocks in the WZW conformal field theory and their dimensions are given by the Verlinde rule. We describe monomial bases for the s-fractur sign and l-fractur sign2 spaces of coinvariants, In particular, we prove that the spaces of coinvariants have the same dimensions when all the points coincide. We establish recurrence relations satisfied by the monomial bases and the corresponding characters of the spaces of coinvariants. For the proof we use filtrations of the s-fractur sign and l-fractur sign 2 modules. The adjoint graded spaces are certain modules on the loop Heisenberg algebra. The recurrence relation is established by using filtrations on these modules.

KW - Affine Lie algebra

KW - Combinatorics

KW - Conformal field theory

UR - http://www.scopus.com/inward/record.url?scp=11144280097&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=11144280097&partnerID=8YFLogxK

U2 - 10.1007/s00029-002-8112-4

DO - 10.1007/s00029-002-8112-4

M3 - Article

AN - SCOPUS:11144280097

VL - 8

SP - 419

EP - 474

JO - Selecta Mathematica, New Series

JF - Selecta Mathematica, New Series

SN - 1022-1824

IS - 3

ER -