无限楔形和随机分割

半无限楔形体导论

An introduction to the half-infinite wedge

在快速回顾了对称群的表示论之后，我们给出了无限对称群的所谓半无限楔形表示所带来的工具的阐述。我们展示了如何可以应用这些来找到几个分布分区的极限形状。我们还简要回顾了可用于计算这些极限形状的变分方法。

Comments related to infinite wedge representations

We study the infinite wedge representation and show how it is related to the universal extension of $g[t,t^{-1}]$ the loop algebra of a complex semi-simple Lie algebra $g$. We also give an elementary proof of the boson-fermion correspondence. Our approach to proving this result is based on a combinatorial construction with partitions combined with an application of the Murnaghan-Nakayama rule.

Dual Infinite Wedge is $\mathrm{GL}_{\infty}$-equivariantly noetherian

We prove the (equivariant) noetherian property for a wide class of varieties generalizing the class of Plucker varieties (Theorem 1). It improves previous results of Draisma-Eggermont who treated the case of bounded Plucker varieties. Key ingredient of our proof is the constructive proof of the equivariant noetherianity for the hyper-Pfaffians (Theorem 36) which implies the equivariant noetherianity of the dual infinite wedge.

Schubert Derivations on the Infinite Wedge Power

The {\em Schubert derivation} is a distinguished Hasse-Schmidt derivation on the exterior algebra of a free abelian group, encoding the formalism of Schubert calculus for all Grassmannians at once. The purpose of this paper is to extend the Schubert derivation to the infinite exterior power of a free ${\mathbb Z}$-module of infinite rank (fermionic Fock space). Classical vertex operators naturally arise from the {\em integration by parts formula}, that also recovers the generating function occurring in the {\em bosonic vertex representation} of the Lie algebra $gl_\infty({\mathbb Z})$, due to …

与无限Gelfand对$(S(2\infty),H(\infty))$有关的分拆上的Z-测度

Z-measures on partitions related to the infinite Gelfand pair $(S(2\infty),H(\infty))$

本文讨论了变形（Jack）参数为2或1/2的剖分上的z-测度。我们提供了一个详细的解释，这些措施的代表理论的起源，他们的作用在调和分析的无限对称群。

关于无限对称群的线性特征标和射影特征标的调和分析的划分测度

On Measures on Partitions Arising in Harmonic Analysis for Linear and Projective Characters of the Infinite Symmetric Group

划分上的z-测度起源于Kerov，Olshanski和Vershik（1993，2004）的作品中无限对称群的线性表示的调和分析问题。Borodin（1997）引入了一个对应于射影表示的类似族。后一种措施存在于严格的分区上（即，具有不同部分的分区），并且z测量值由所有分区支持。在本说明中，我们描述了这两个家庭的措施，使用著名的加倍转移杨图之间的一些组合关系。