A character formula for certain representations of loop groups based on non-simply connected Lie groups

On tame strongly simply connected algebras

In this survey we present the criterion for tameness of strongly simply connected algebras due to Brüstle, de la Peña and Skowroński. We recall relevant concepts of representation theory and discuss some applications and connections to other problems.

The fundamental group of an algebra with strongly simply connected Galois covering

In this work, we prove that if a triangular algebra $A$ admits a strongly simply connected universal Galois covering for a given presentation then the fundamental group associated to this presentation is free.

On $τ$-tilting finite simply connected algebras

We show that $τ$-tilting finite simply connected algebras are representation-finite. Then, some related algebras are considered, including iterated tilted algebras, tubular algebras and so on. We also prove that the $τ$-tilting finiteness of non-sincere algebras can be reduced to that of sincere algebras. This motivates us to give a complete list of $τ$-tilting finite sincere simply connected algebras.

An Erdos-Turan Inequality For Compact Simply-Connected Semisimple Lie Groups

The classical Erd{\" o}s-Turan Inequality bounds how far a sequence of points in the circle is from being equidistributed in terms of its exponential moments. We prove an analogous inequality for all compact simply-connected semisimple Lie groups, bounding how far a sequence is from being equidistributed in the conjugacy classes of the group in terms of the moments of irreducible characters.

The representation ring of a simply-connected Lie group as a lambda-ring

Adams and Conway have stated without proof a result which says, roughly speaking, that the representation ring $R(G)$ of a compact, connected Lie group $G$ is generated as a $λ$-ring by elements in 1-to-1 correspondance with the branches of the Dynkin diagram. In this note we present an elementary proof of this.

有限表示型单连通代数的张量积

Representation-finite tensor product of simply connected algebras

本文确定了当$A$和$B$均为至少含三个单模的单连通代数时，其张量积$A\otimes B$的有限表示性。