Lattice of dominant weights of affine Kac-Moody algebras

Closed sets of real roots in Kac-Moody root systems

In this note, we provide a complete description of the closed sets of real roots in a Kac-Moody root system.

仿射Kac-Moody代数的实型和有穷级自同构--一种新方法的概要

Real forms and finite order automorphisms of affine Kac-Moody algebras - an outline of a new approach

给出了仿射Kac-Moody代数实型和有穷级自同构分类的一种新方法。

Toward a Jacobson--Morozov theorem for Kac--Moody Lie algebras

For a finite-dimensional semisimple Lie algebra $\mathfrak{g}$, the Jacobson--Morozov theorem gives a construction of subalgebras $\mathfrak{sl}_2 \subset \mathfrak{g}$ corresponding to nilpotent elements of $\mathfrak{g}$. In this note, we propose an extension of the Jacobson--Morozov theorem to the symmetrizable Kac--Moody setting and give a proof of this generalization in the case of rank two hyperbolic Kac--Moody algebras. We also give a proof for an arbitrary symmetrizable Kac--Moody algebra under some stronger restrictions.

仿射Kac-Moody代数的一类标准子代数

A certain class of standard subalgebras of affine Kac-Moody algebras

将有限维单李代数的标准子代数理论推广到无限维李代数。构造并刻画了仿射Kac-Moody代数的一类标准子代数。

An algorithm for computing root multiplicities in Kac-Moody algebras

Root multiplicities encode information about the structure of Kac-Moody algebras, and appear in applications as far-reaching as string theory and the theory of modular functions. We provide an algorithm based on the Peterson recurrence formula to compute multiplicities, and argue that it is more efficient than the naive algorithm.

秩2双曲Kac-Moody代数根重数的组合方法

A combinatorial approach to root multiplicities of rank 2 hyperbolic Kac-Moody algebras

本文利用Dyck路的组合学研究了秩2双曲Kac-Moody代数的根重数。

仿射Kac-Moody代数的正则子代数

Regular subalgebras of affine Kac-Moody algebras

利用仿射Kac-Moody代数的根系对正则子代数进行了分类.在这个过程中，我们建立了一个子代数的根系总是代数的根系与它的根格的子格的交。我们还讨论了双曲Kac-Moody代数的正则子代数和仿射Kac-Moody代数的共形不变子代数的研究中的应用。

绝对不可分解表示与Kac-Moody李代数（附中岛平的附录）

Absolutely indecomposable representations and Kac-Moody Lie algebras (with an appendix by Hiraku Nakajima)

Kac的一个猜想指出，在有限域上计算一个具有给定维数向量的多项式的绝对不可分解表示的个数的多项式具有正系数，而且它的常数项等于相应Kac-Moody李代数中相应根的重数.本文对不可分维数向量证明了这些定理。

双曲Kac-Moody代数$E_{10}$的自守修正

Automorphic correction of the hyperbolic Kac-Moody algebra $E_{10}$

本文研究了双曲Kac-Moody代数$E_{10}$的自守修正问题，利用O（10，2）的Borcherds积与$SL_2(\mathbb Z)$的权为-4的弱全纯模形式相连接.我们还澄清了Lorentzian Kac-Moody代数的自守修正的一些方面，并给出了启发性的理由，期望每个Lorentzian Kac-Moody代数有一个自守修正。

双曲Kac-Moody代数的双曲子代数

Hyperbolic subalgebras of hyperbolic Kac-Moody algebras

通过外尔群研究了双曲Kac-Moody代数的正则双曲子代数.对双曲Kac-Moody代数的外尔群之间的所有子群关系进行了分类，证明了对于每一对群和子群，至少存在一对对应的代数和子代数.给出了双曲Kac-Moody代数的正则双曲子代数的有限分类算法。

Some branching formulas for Kac--Moody Lie algebras

In this paper we give some branching rules for the fundamental representations of Kac--Moody Lie algebras associated to $T$-shaped graphs. These formulas are useful to describe generators of the generic rings for free resolutions of length three described in [JWm16]. We also make some conjectures about the generic rings.

Conversations with Flaschka: Kac-Moody groups and Verblunsky coefficients

In this paper we discuss two items which in one way or another originated from conversations with Hermann Flaschka and his students. The first is an application of the Toda lattice to the question of whether there exists a complex Lie group (with certain properties) associated to an indefinite type Kac-Moody Lie algebra. The second concerns a new example of the Verblunsky correspondence.