Cylindric skew Schur functions
By Peter R. W. McNamara. 2004
53 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/0470038c0494306cfd3dfce6f61dc78019e2d4fd
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In Algebra and Number Theory
- Thomas Lam
- Mark Shimozono
- Anne Schilling
- Jennifer Morse
- Luc Lapointe
- Mike Zabrocki
- Stephanie van Willigenburg
- Christine Bessenrodt
In Discrete Mathematics and Combinatorics
- Thomas Lam
- Mark Shimozono
- Anne Schilling
- Jennifer Morse
- Luc Lapointe
- Mike Zabrocki
- Stephanie van Willigenburg
- Kurt W. Luoto
In Geometry and Topology
- Thomas Lam
- Mark Shimozono
- Anne Schilling
- Jennifer Morse
- Luc Lapointe
- Mike Zabrocki
- Stephanie van Willigenburg
- Kurt W. Luoto
Citations in the corpus
- Skew quasisymmetric Schur functions and noncommutative Schur functions (2010, background): “the symmetric group [41, 61], k-Schur functions connected to the enumeration of Gromov-Witten invariants [37], cylindric Schur functions [44], shifted Schur functions related to the representation theory of GL(n) [48], and factorial Schur functions that are special cases of double Schubert polynomia”
- k-Schur Functions and Affine Schubert Calculus (2013, background): “(Cylindric Schur functions [133, 121]) Let C(k, n) denote the set of lattice paths p in Z2 where every step either goes up or to the right, and which is invariant under the translation (x, y) 7→ (x + n − k, y + k).”
- Affine Stanley symmetric functions (2005, background): “See [25] for a detailed discussion of this.”