In this paper we compute the radial parts of the projections of orbital measures for the compact Lie groups of B, C, and D type, extending previous results obtained for the case of the unitary group by Olshanski and Faraut. Applying the method of Faraut, we show that the radial part of the projection of an orbital measure is expressed in terms of a B-spline with knots located symmetrically with respect to zero.
The cell structure of spaces M2,1 and M3,1 is considered. M2,1 and M3,1 are the spaces of complex curves of genus 2 and 3 with one marked point. For the space M2,1 nine cells of the highest dimension 8 are described and their adjacency is studied. For the space M3,1 the list of 1726 cells of the highest dimension 14 (and their orientation) is obtained. Also is obtained the list of adjacent couples of cells.
M. Vuletic has recently found a two-parameter generalization of MacMahon’s formula. In this paper we show that the coefficients in her formula are the Betti numbers of certain subvarieties in the moduli space of sheaves on the projective plane.