Pavle Pandžić

activity

20102026

most citedBGG complexes in singular infinitesimal character for type A

6 citations · 30 across the 17 of their papers we have counts for

collaborators

21 papers

math.RT2026

On the $K$ -types of certain families of unitary highest weight representations of Hermitian Lie groups

Pavle Pand\v zić, Genkai Zhang

Let $(g, k)$ be the complexication of a Hermitian symmetric pair and let $γ_{1} < \dots < γ_{r}$ be the Harish-Chandra strongly orthogonal roots, with $γ_{1}$ the lowes…

math.RT2026

Symmetric spaces and skew multiplicity free representations

Kieran Calvert, Kyo Nishiyama, Pavle Pandžić

Let $G$ be a non-compact connected reductive real Lie group and $P$ its parabolic subgroup. We give a list of equivalent conditions for $P$ to have an abelian unipotent radic…

math.RT2026

Toric degeneration for hybrid qudit spaces

Jing-Song Huang, Soo Teck Lee, Pavle Pandžić

We consider covariant algebras attached to certain hybrid qudit spaces. We describe these algebras in terms of generators and relations, and we show they are flat deformations of c…

math.RT2025

Clifford algebra analogue of Cartan's theorem for symmetric pairs

Kieran Calvert, Karmen Grizelj, Andrey Krutov +1

We extend Kostant's results about $g$ -invariants in the Clifford algebra $C l (g)$ of a complex semisimple Lie algebra $g$ to the relative case of $\…

math.RT2025★ 1 cited

On the classification of unitary highest weight modules in the exceptional cases

Pavle Pandžić, Ana Prlić, Gordan Savin +2

In our previous paper, we gave a complete classification of the unitary highest weight modules for the universal covers of the Lie groups $S p (2 n, R), S O^{*} (2 n)$ and $SU(p…

math.QA2024

Braided coproduct, antipode and adjoint action for $U_{q} (s l_{2})$

Pavle Pandžić, Petr Somberg

Motivated by our attempts to construct an analogue of the Dirac operator in the setting of $U_{q} (sl_{n})$ , we write down explicitly the braided coproduct, antipode, and adj…

math.QA2024★ 1 cited

Quantised $sl_{2}$ -differential algebras

Andrey Krutov, Pavle Pandžić

We propose a definition of a quantised $sl_{2}$ -differential algebra and show that the quantised exterior algebra (defined by Berenstein and Zwicknagl) and the quantised C…

math.RT2023

On the classification of unitary highest weight modules

Pavle Pandžić, Ana Prlić, Vladimír Souček +1

In the 1980s, Enright, Howe and Wallach [EHW] and independently Jakobsen [J] gave a complete classification of the unitary highest weight modules. In this paper we give a more dire…

math.RT2022★ 4 cited

Dirac inequality for highest weight Harish-Chandra modules II

Pavle Pandžić, Ana Prlić, Vladimír Souček +1

Let $G$ be a connected simply connected noncompact exceptional simple Lie group of Hermitian type. In this paper, we work with the Dirac inequality which is a very useful tool for…

math.RT2022★ 3 cited

Dirac inequality for highest weight Harish-Chandra modules I

Pavle Pandžić, Ana Prlić, Vladimír Souček +1

Let $G$ be a connected simply connected noncompact classical simple Lie group of Hermitian type. Then $G$ has unitary highest weight representations. The proof of the classificatio…

math.RT2022★ 1 cited

Cubic Dirac operator for $U_{q} (sl_{2})$

Andrey Krutov, Pavle Pandžić

We construct the $q$ -deformed Clifford algebra of $sl_{2}$ and study its properties. This allows us to define the $q$ -deformed noncommutative Weil algebra $\mathcal{W}_q(\…

math.RT2021

Representation theoretic embedding of twisted Dirac operators

Salah Mehdi, Pavle Pandzic

Let $G$ be a non-compact connected semisimple real Lie group with finite center. Suppose $L$ is a non-compact connected closed subgroup of $G$ acting transitively on a symmetric sp…

math.RT2017

Computing the associatied cycles of certain Harish-Chandra modules

Salah Mehdi, Pavle Pandzic, David Vogan +1

Let $G_{R}$ be a simple real linear Lie group with maximal compact subgroup $K_{R}$ and assume that $rank (G_{R}) = rank (K_{R})$ . In \cite{…

math.RT2017

Dirac Index and associated cycles of Harish-Chandra modules

Salah Mehdi, Pavle Pandzic, David Vogan +1

Let $G_{R}$ be a simple real linear Lie group with maximal compact subgroup $K_{R}$ and assume that $rank (G_{R}) = rank (K_{R})$ . For any r…

math.RT2017★ 4 cited

Dirac operator and its cohomology for the quantum group $U_{q} (sl_{2})$

Pavle Pandžić, Petr Somberg

We introduce a Dirac operator $D$ for the quantum group $U_{q} (sl_{2})$ , as an element of the tensor product of $U_{q} (sl_{2})$ with the Clifford algebra on two gener…

math.DG2016★ 6 cited

BGG complexes in singular infinitesimal character for type A

Pavle Pandzic, Vladimir Soucek

We give a geometric construction of the BGG resolutions in singular infinitesimal character in the case of 1-graded complex Lie algebras of type A.

math.RT2016★ 4 cited

Dirac Index and Twisted Characters

Dan Barbasch, Pavle Pandzic, Peter Trapa

Let G be a real reductive Lie group with maximal compact sub- group K. We generalize the usual notion of Dirac index to a twisted version, which is nontrivial even in case G and K…

math.RT2015★ 1 cited

Branching problems and $s l (2, C)$ -actions

Pavle Pandžić, Petr Somberg

We study certain $s l (2, C)$ -actions associated to specific examples of branching of scalar generalized Verma modules for compatible pairs $({\mathf…

math.RT2015★ 1 cited

Translation principle for Dirac index

Salah Mehdi, Pavle Pandžić, David A. Vogan

Let $G$ be a finite cover of a closed connected transpose-stable subgroup of $GL(n,\bR)$ with complexified Lie algebra $\frg$. Let $K$ be a maximal compact subgroup of $G$ , and ass…

math.RT2013★ 4 cited

Higher Dirac cohomology of modules with generalized infinitesimal character

Pavle Pandžić, Petr Somberg

We modify the definition of Dirac cohomology in such a way that the standard properties of the usual Dirac cohomology, valid for modules with infinitesimal character, become valid…

math.RT2010

Dirac cohomology and unipotent representations of complex groups

Dan Barbasch, Pavle Pandžić

This paper studies unitary representations with Dirac cohomology for complex groups, in particular relations to unipotent representations

On the K-types of certain families of unitary highest weight representations of Hermitian Lie groups

Symmetric spaces and skew multiplicity free representations

Toric degeneration for hybrid qudit spaces

Clifford algebra analogue of Cartan's theorem for symmetric pairs

On the classification of unitary highest weight modules in the exceptional cases

Braided coproduct, antipode and adjoint action for Uq​(sl2​)

Quantised sl2​-differential algebras

On the classification of unitary highest weight modules

Dirac inequality for highest weight Harish-Chandra modules II

Dirac inequality for highest weight Harish-Chandra modules I

Cubic Dirac operator for Uq​(sl2​)

Representation theoretic embedding of twisted Dirac operators

Computing the associatied cycles of certain Harish-Chandra modules

Dirac Index and associated cycles of Harish-Chandra modules

Dirac operator and its cohomology for the quantum group Uq​(sl2​)

BGG complexes in singular infinitesimal character for type A

Dirac Index and Twisted Characters

Branching problems and sl(2,C)-actions

Translation principle for Dirac index

Higher Dirac cohomology of modules with generalized infinitesimal character

Dirac cohomology and unipotent representations of complex groups

On the $K$ -types of certain families of unitary highest weight representations of Hermitian Lie groups

Braided coproduct, antipode and adjoint action for $U_{q} (s l_{2})$

Quantised $sl_{2}$ -differential algebras

Cubic Dirac operator for $U_{q} (sl_{2})$

Dirac operator and its cohomology for the quantum group $U_{q} (sl_{2})$

Branching problems and $s l (2, C)$ -actions