Cylindric skew Schur functions

Details Cylindric skew Schur functions Cylindric skew Schur functions

2004-10-13

arxiv.org/abs/math/0410301v2

Advances in Mathematics 205 (2006), 275-312

Mathematics

Combinatorics

32 pages, 14 figures. Minor expository improvements. Version to appear in Advances in Mathematics

Scientific paper

Cylindric skew Schur functions, which are a generalisation of skew Schur functions, arise naturally in the study of P-partitions. Also, recent work of A. Postnikov shows they have a strong connection with a problem of considerable current interest: that of finding a combinatorial proof of the non-negativity of the 3-point Gromov-Witten invariants. After explaining these motivations, we study cylindric skew Schur functions from the point of view of Schur-positivity. Using a result of I. Gessel and C. Krattenthaler, we generalise a formula of A. Bertram, I. Ciocan-Fontanine and W. Fulton, thus giving an expansion of an arbitrary cylindric skew Schur function in terms of skew Schur functions. While we show that no non-trivial cylindric skew Schur functions are Schur-positive, we conjecture that this can be reconciled using the new concept of cylindric Schur-positivity.

Affiliated with

Also associated with

No associations

Rating

Cylindric skew Schur functions 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 Cylindric skew Schur functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Cylindric skew Schur functions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-136693