S. Afentoulidis-Almpanis

activity

20222026

collaborators

6 papers

math.RT2026

Structure and Representation Theory of basic simple $Z_{2} \times Z_{2}$ -graded color Lie algebras

Spyridon Afentoulidis-Almpanis

We adapt methods from the theory of complex semisimple Lie algebras to develop a root theory for a class of simple $Z_{2} \times Z_{2}$ -graded (color) Lie algebras, w…

math.RT2025

Dirac operators for algebraic families

Spyridon Afentoulidis-Almpanis, Eyal Subag

We introduce algebraic families of Dirac operators for the deformation family (and other related families) associated with a real reductive Lie group that interpolates the reductiv…

math.RT2025

Tensor product decomposition for rank-one spin groups I : unitary principal series representations

Spyridon Afentoulidis-Almpanis, Gang Liu

We provide an explicit direct integral decomposition for the tensor product representation $π_{1} \otimes π_{2}$ of the rank one spin group $Spin (n, 1)$ whenever $π_{1}$ …

math.RT2023

Dirac cohomology and $Θ$ -correspondence for complex dual pairs

Spyridon Afentoulidis-Almpanis, Gang Liu, Salah Mehdi

We study the behavior of Dirac cohomology under Howe's $Θ$ -correspondence in the case of complex reductive dual pairs. More precisely, if $(G_{1}, G_{2})$ is a complex reductive dual pa…

math.RT2022

Noncubic Dirac operators for finite dimensional modules

Spyridon Afentoulidis-Almpanis

We study the decomposition into irreducibles of the kernel of noncubic Dirac operators attached to finite-dimensional modules. We compare this decomposition with features of Kostan…

math.RT2022

Dirac cohomology for the BGG category $O$

Spyridon Afentoulidis-Almpanis

We study Dirac cohomology $H_{D}^{g, h} (M)$ for modules belonging to category $O$ of a finite dimensional complex semisimple Lie algebra. We prove Voga…

Structure and Representation Theory of basic simple Z2​×Z2​-graded color Lie algebras

Dirac operators for algebraic families

Tensor product decomposition for rank-one spin groups I : unitary principal series representations

Dirac cohomology and Θ-correspondence for complex dual pairs

Noncubic Dirac operators for finite dimensional modules

Dirac cohomology for the BGG category O

Structure and Representation Theory of basic simple $Z_{2} \times Z_{2}$ -graded color Lie algebras

Dirac cohomology and $Θ$ -correspondence for complex dual pairs

Dirac cohomology for the BGG category $O$