Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2009-04-27
Theor.Math.Phys.166:1-22,2011
Physics
High Energy Physics
High Energy Physics - Theory
21 pages
Scientific paper
10.1007/s11232-011-0001-6
We define cut-and-join operator in Hurwitz theory for merging of two branching points of arbitrary type. These operators have two alternative descriptions:(i) they have the GL characters as eigenfunctions and the symmetric-group characters as eigenvalues; (ii) they can be represented as differential operators of the $W$-type (in particular, acting on the time-variables in the Hurwitz-Kontsevich tau-function). The operators have the simplest form if expressed in terms of the matrix Miwa-variables. They form an important commutative associative algebra, a Universal Hurwitz Algebra, generalizing all group algebra centers of particular symmetric groups which are used in description of the Universal Hurwitz numbers of particular orders. This algebra expresses arbitrary Hurwitz numbers as values of a distinguished linear form on the linear space of Young diagrams, evaluated at the product of all diagrams, which characterize particular ramification points of the covering.
Mironov Aleksej
Morozov Alexander
Natanzon Sergey
No associations
LandOfFree
Complete Set of Cut-and-Join Operators in Hurwitz-Kontsevich Theory does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Complete Set of Cut-and-Join Operators in Hurwitz-Kontsevich Theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Complete Set of Cut-and-Join Operators in Hurwitz-Kontsevich Theory will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-323288