The Poset of k Shapes and Branching Rules for k Schur Functions is popular PDF and ePub book, written by Thomas Lam in 2013-04-22, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, The Poset of k Shapes and Branching Rules for k Schur Functions can be Read Online from any device for your convenience.
The Poset of k Shapes and Branching Rules for k Schur Functions Book PDF Summary
The authors give a combinatorial expansion of a Schubert homology class in the affine Grassmannian $\mathrm{Gr}_{\mathrm{SL}_k}$ into Schubert homology classes in $\mathrm{Gr}_{\mathrm{SL}_{k+1}}$. This is achieved by studying the combinatorics of a new class of partitions called $k$-shapes, which interpolates between $k$-cores and $k+1$-cores. The authors define a symmetric function for each $k$-shape, and show that they expand positively in terms of dual $k$-Schur functions. They obtain an explicit combinatorial description of the expansion of an ungraded $k$-Schur function into $k+1$-Schur functions. As a corollary, they give a formula for the Schur expansion of an ungraded $k$-Schur function.
Detail Book of The Poset of k Shapes and Branching Rules for k Schur Functions PDF
- Author : Thomas Lam
- Release : 22 April 2013
- Publisher : American Mathematical Soc.
- ISBN : 9780821872949
- Genre : Mathematics
- Total Page : 113 pages
- Language : English
- PDF File Size : 14,6 Mb
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