### Abstract

Let Σ denote a closed oriented surface. There is a natural action of the group Diff^{+}(Σ) on sections of the chiral determinant line over the space of gauge equivalence classes of connections. The question we address is whether this action is unitarizable. We introduce a SDiff-equivariant regularization, and we prove the existence of, and explicitly compute, the limit as the regularization is removed. The SDiff unitary representations that arise, both by regularization and after removing the regularization, appear to be new.

Original language | English (US) |
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Pages (from-to) | 177-199 |

Number of pages | 23 |

Journal | Pacific Journal of Mathematics |

Volume | 193 |

Issue number | 1 |

State | Published - Mar 2000 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**On the action of the group of diffeomorphisms of a surface on sections of the determinant line bundle.** / Pickrell, Douglas M.

Research output: Contribution to journal › Article

*Pacific Journal of Mathematics*, vol. 193, no. 1, pp. 177-199.

}

TY - JOUR

T1 - On the action of the group of diffeomorphisms of a surface on sections of the determinant line bundle

AU - Pickrell, Douglas M

PY - 2000/3

Y1 - 2000/3

N2 - Let Σ denote a closed oriented surface. There is a natural action of the group Diff+(Σ) on sections of the chiral determinant line over the space of gauge equivalence classes of connections. The question we address is whether this action is unitarizable. We introduce a SDiff-equivariant regularization, and we prove the existence of, and explicitly compute, the limit as the regularization is removed. The SDiff unitary representations that arise, both by regularization and after removing the regularization, appear to be new.

AB - Let Σ denote a closed oriented surface. There is a natural action of the group Diff+(Σ) on sections of the chiral determinant line over the space of gauge equivalence classes of connections. The question we address is whether this action is unitarizable. We introduce a SDiff-equivariant regularization, and we prove the existence of, and explicitly compute, the limit as the regularization is removed. The SDiff unitary representations that arise, both by regularization and after removing the regularization, appear to be new.

UR - http://www.scopus.com/inward/record.url?scp=0040185992&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0040185992&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0040185992

VL - 193

SP - 177

EP - 199

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

SN - 0030-8730

IS - 1

ER -