Zobrazeno 1 - 10
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pro vyhledávání: '"Pandzic, Pavle"'
We show how to use Clifford algebra techniques to describe the de Rham cohomology ring of equal rank compact symmetric spaces $G/K$. In particular, for $G/K=U(n)/U(k)\times U(n-k)$, we obtain a new way of multiplying Schur polynomials, i.e., computin
Externí odkaz:
http://arxiv.org/abs/2411.11663
Autor:
Pandžić, Pavle, Somberg, Petr
Motivated by our attempts to construct an analogue of the Dirac operator in the setting of $U_q(\mathfrak{sl}_n)$, we write down explicitly the braided coproduct, antipode, and adjoint action for quantum algebra $U_q(\mathfrak{sl}_2)$. The braided ad
Externí odkaz:
http://arxiv.org/abs/2404.06871
Autor:
Krutov, Andrey, Pandžić, Pavle
We propose a definition of a quantised $\mathfrak{sl}_2$-differential algebra and show that the quantised exterior algebra (defined by Berenstein and Zwicknagl) and the quantised Clifford algebra (defined by the authors) of $\mathfrak{sl}_2$ are natu
Externí odkaz:
http://arxiv.org/abs/2403.08521
We study various kinds of Grassmannians or Lagrangian Grassmannians over $\mathbb{R}$, $\mathbb{C}$ or $\mathbb{H}$, all of which can be expressed as $\mathbb{G}/\mathbb{P}$ where $\mathbb{G}$ is a classical group and $\mathbb{P}$ is a parabolic subg
Externí odkaz:
http://arxiv.org/abs/2310.04839
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 direct and elementary proof of the same result for the (universal covers o
Externí odkaz:
http://arxiv.org/abs/2305.15892
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 the classification of unitary highest weight modules.
Comment: 26
Comment: 26
Externí odkaz:
http://arxiv.org/abs/2209.15331
Autor:
Krutov, Andrey, Pandžić, Pavle
We construct the $q$-deformed Clifford algebra of $\mathfrak{sl}_2$ and study its properties. This allows us to define the $q$-deformed noncommutative Weil algebra $\mathcal{W}_q(\mathfrak{sl}_2)$ for $U_q(\mathfrak{sl}_2)$ and the corresponding cubi
Externí odkaz:
http://arxiv.org/abs/2209.09591
Autor:
Mehdi, Salah, Pandzic, Pavle
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 space $G/H$ such that $L\cap H$ is compact. We study the action on $L/L\
Externí odkaz:
http://arxiv.org/abs/2102.03562
Let $G_{\mathbb{R}}$ be a simple real linear Lie group with maximal compact subgroup $K_{\mathbb{R}}$ and assume that ${\rm rank}(G_\mathbb{R})={\rm rank}(K_\mathbb{R})$. In \cite{MPVZ} we proved that for any representation $X$ of Gelfand-Kirillov di
Externí odkaz:
http://arxiv.org/abs/1712.04173
Let $G_{\mathbb{R}}$ be a simple real linear Lie group with maximal compact subgroup $K_{\mathbb{R}}$ and assume that ${\rm rank}(G_\mathbb{R})={\rm rank}(K_\mathbb{R})$. For any representation $X$ of Gelfand-Kirillov dimension $\frac{1}{2} {\rm dim}
Externí odkaz:
http://arxiv.org/abs/1712.04169