The Horn recursions for Schur P- and Q- functions </HEAD> <BODY BGCOLOR="#FFFFFF"> <HR><img hspace=10 align=center src="../images/ams-logo.gif"> <BR clear=all><HR> <TABLE> <TR> <TD> <A HREF="http://www.ams.org/amsmtgs/2120_program.html">AMS Eastern Sectional Meeting in <b>Annandale-on-Hudson, NY</b></A><BR> 8-9 October 2005 <P> <B>Title:</B> The Horn recursions for Schur <I>P</I>- and <I>Q</I>- functions.<BR> <B>Session Name:</B> Special Session on Algebraic and Geometric Combinatorics <P> <B>Author:</B> K. Purbhoo<BR> <B>Author:</B> F. Sottile<BR> <b>Abstract:</b><br> Work of Klyachko and of Knutson and Tao proved Horn's recursion for non-zero Littlewood-Richardson coefficients: A Littlewood-Richardson coefficient is non-zero if and only if it satisfies linear inequalities imposed by smaller Littlewood Richardson coefficients. Belkale gave a proof of this recursion using geometry. In this talk, I will discuss similar recursions for the analog of the Littlewood-Richardson coefficients for Schur <I>P</I>- and <I>Q</I>- functions, obtained by generalizing Belkale's work. While the coefficients for each type differ only by a (known) power of 2, the geometry of cominuscule flag manifolds gives two different recursions, one for each type. </TD> </TR></TABLE> <BR><BR><HR><BR> </BODY> </HTML>