Zobrazeno 1 - 10
of 25
pro vyhledávání: '"Zhang, Sylvester W."'
Autor:
Zhang, Sylvester W.
We show that the Hilbert space with basis indexed by infinite permutations and the cohomology ring of the infinite flag variety can be seen as representations of the Heisenberg algebra, which are isomorphic using the back-stable Schubert polynomials.
Externí odkaz:
http://arxiv.org/abs/2409.20389
We introduce a $q$-analog of the higher continued fractions introduced by the last three authors in a previous work (together with Gregg Musiker), which are simultaneously a generalization of the $q$-rational numbers of Morier-Genoud and Ovsienko. Th
Externí odkaz:
http://arxiv.org/abs/2408.06902
Graph LP algebras are a generalization of cluster algebras introduced by Lam and Pylyavskyy. We provide a combinatorial proof of positivity for certain cluster variables in these algebras. This proof uses a hypergraph generalization of snake graphs,
Externí odkaz:
http://arxiv.org/abs/2312.12313
Snake graphs are a class of planar graphs that are important in the theory of cluster algebras. Indeed, the Laurent expansions of the cluster variables in cluster algebras from surfaces are given as weight generating functions for 1-dimer covers (or
Externí odkaz:
http://arxiv.org/abs/2306.14389
For an arc on a bordered surface with marked points, we associate a holonomy matrix using a product of elements of the supergroup $\mathrm{OSp}(1|2)$, which defines a flat $\mathrm{OSp}(1|2)$-connection on the surface. We show that our matrix formula
Externí odkaz:
http://arxiv.org/abs/2208.13664
Autor:
Curran, Michael J., Frechette, Claire, Yost-Wolff, Calvin, Zhang, Sylvester W., Zhang, Valerie
We introduce a solvable lattice model for supersymmetric LLT polynomials, also known as super LLT polynomials, based upon particle interactions in super n-ribbon tableaux. Using operators on a Fock space, we prove a Cauchy identity for super LLT poly
Externí odkaz:
http://arxiv.org/abs/2110.07597
In a recent paper, the authors gave combinatorial formulas for the Laurent expansions of super $\lambda$-lengths in a marked disk, generalizing Schiffler's $T$-path formula. In the present paper, we give an alternate combinatorial expression for thes
Externí odkaz:
http://arxiv.org/abs/2110.06497
Publikováno v:
SIGMA 18 (2022), 089, 30 pages
LP algebras, introduced by Lam and Pylyavskyy, are a generalization of cluster algebras. These algebras are known to have the Laurent phenomenon, but positivity remains conjectural. Graph LP algebras are finite LP algebras encoded by a graph. For the
Externí odkaz:
http://arxiv.org/abs/2107.14785
Publikováno v:
SIGMA 17 (2021), 080, 34 pages
Motivated by the definition of super-Teichm\"uller spaces, and Penner-Zeitlin's recent extension of this definition to decorated super-Teichm\"uller space, as examples of super Riemann surfaces, we use the super Ptolemy relations to obtain formulas f
Externí odkaz:
http://arxiv.org/abs/2102.09143
Rowmotion is an invertible operator on the order ideals of a poset which has been extensively studied and is well understood for the rectangle poset. In this paper, we show that rowmotion is equivariant with respect to a bijection of Hamaker, Patrias
Externí odkaz:
http://arxiv.org/abs/2002.04810