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pro vyhledávání: '"Dobrev, V. K."'
Autor:
Dobrev, V. K.
Langlands duality is one of the most influential topics in mathematical research. It has many different appearances and influential subtopics. Yet there is a topic that until now seems unrelated to the Langlands program. That is the topic of invarian
Externí odkaz:
http://arxiv.org/abs/2411.16432
Autor:
Dobrev, V. K.
We construct representations of the quantum algebras ~$U_{q{\bf q}}(gl(n))$ and ~$U_{q{\bf q}}(sl(n))$~ which are in duality with the multiparameter quantum groups ~$GL_{q{\bf q}}(n)$, ~$SL_{q{\bf q}}(n)$,~ respectively. These objects depend on ~$n(n
Externí odkaz:
http://arxiv.org/abs/2404.09843
Autor:
Aizawa, N., Dobrev, V. K.
Publikováno v:
I. J. Mod. Phys. A, 39 (2024) 2450022
In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebras $sp(n,1)$. Our choice of these algebras is motivated by the fact that they belong to a narrow class
Externí odkaz:
http://arxiv.org/abs/2312.17000
Autor:
Dobrev, V. K.
Publikováno v:
Symmetry 2022, 14, (4) 660
In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebra $G_{2(2)}$. We use both the minimal and the maximal Heisenberg parabolic subalgebras. We give the ma
Externí odkaz:
http://arxiv.org/abs/2112.13729
Autor:
Dobrev, V. K.
Publikováno v:
World Scientific, November 2022
In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact exceptional Lie algebra $F"_4$ which is the split rank one form of the exceptional Lie algebra $F_4$. We cla
Externí odkaz:
http://arxiv.org/abs/2109.08395
Autor:
Aizawa, N., Dobrev, V. K.
Publikováno v:
Mod. Phys. Lett. A 37, 2250067 (2022)
In the present paper we construct explicitly the intertwining differential operators for the Jacobi algebra ${\cal G}_2.$ For the construction we use the singular vectors of the Verma modules over ${\cal G}_2$ which we have constructed earlier. We co
Externí odkaz:
http://arxiv.org/abs/2108.12813
Publikováno v:
J. Phys. A: Math. Theor. 54 475202 (2021)
In the present paper we study the representations of the Jacobi algebra. More concretely, we define, analogously to the case of semi-simple Lie algebras, the Verma modules over the Jacobi algebra ${\cal G}_2$. We study their reducibility and give exp
Externí odkaz:
http://arxiv.org/abs/2105.07173
Autor:
Dobrev, V. K.
The main purpose of the present paper is to lay the foundations of generalizing the AdS/CFT (holography) idea beyond the conformal setting. The main tool is to find suitable realizations of the bulk and boundary via group theory. We use all ten famil
Externí odkaz:
http://arxiv.org/abs/2009.12582
Autor:
Dobrev, V. K.
In the present paper we continue the project of systematic classification and construction of invariant differential operators for non-compact semisimple Lie groups. This time we make the stress on one of the main building blocks, namely the Verma mo
Externí odkaz:
http://arxiv.org/abs/1912.06443