2012年5月
Generalized string equations for double Hurwitz numbers
JOURNAL OF GEOMETRY AND PHYSICS
- 巻
- 62
- 号
- 5
- 開始ページ
- 1135
- 終了ページ
- 1156
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1016/j.geomphys.2011.12.005
- 出版者・発行元
- ELSEVIER SCIENCE BV
The generating function of double Hurwitz numbers is known to become a tau function of the Toda hierarchy. The associated Lax and Orlov-Schulman operators turn out to satisfy a set of generalized string equations. These generalized string equations resemble those of c = 1 string theory except that the Orlov-Schulman operators are contained therein in an exponentiated form. These equations are derived from a set of intertwining relations for fermion bilinears in a two-dimensional free fermion system. The intertwiner is constructed from a fermionic counterpart of the cut-and-join operator. A classical limit of these generalized string equations is also obtained. The so-called Lambert curve emerges in a specialization of its solution. This seems to be another way of deriving the spectral curve of the random matrix approach to Hurwitz numbers. (C) 2011 Elsevier B.V. All rights reserved.
- リンク情報
- ID情報
-
- DOI : 10.1016/j.geomphys.2011.12.005
- ISSN : 0393-0440
- Web of Science ID : WOS:000302527300015