Theta and Heisenberg Groups

1992 ◽  
pp. 147-181
Author(s):  
Herbert Lange ◽  
Christina Birkenhake
Keyword(s):  
Heisenberg Groups

scholarly journals Counting and equidistribution in quaternionic Heisenberg groups

2021 ◽  
pp. 1-38
Author(s):  
JOUNI PARKKONEN ◽  
FRÉDÉRIC PAULIN
Keyword(s):  
Hyperbolic Geometry ◽  
Quaternion Algebra ◽  
Rational Points ◽  
Hyperbolic Spaces ◽  
Heisenberg Groups ◽  
Arithmetic Groups ◽  
Hermitian Forms ◽  
Dimension 2 ◽  
Counting Formula ◽  
The Relationship

Abstract We develop the relationship between quaternionic hyperbolic geometry and arithmetic counting or equidistribution applications, that arises from the action of arithmetic groups on quaternionic hyperbolic spaces, especially in dimension 2. We prove a Mertens counting formula for the rational points over a definite quaternion algebra A over ${\mathbb{Q}}$ in the light cone of quaternionic Hermitian forms, as well as a Neville equidistribution theorem of the set of rational points over A in quaternionic Heisenberg groups.

scholarly journals Quantum Heisenberg groups and sklyanin algebras

1994 ◽  
Vol 31 (3) ◽  
pp. 167-177 ◽  
Author(s):  
Nicol�s Andruskiewitsch ◽  
Jorge Devoto ◽  
Alejandro Tiraboschi
Keyword(s):  
Heisenberg Groups ◽  
Sklyanin Algebras

scholarly journals Finite Heisenberg groups in quiver gauge theories

2006 ◽  
Vol 747 (3) ◽  
pp. 436-454 ◽  
Author(s):  
Benjamin A. Burrington ◽  
James T. Liu ◽  
Leopoldo A. Pando Zayas
Keyword(s):  
Gauge Theories ◽  
Heisenberg Groups

Smoothness of Lipschitz minimal intrinsic graphs in Heisenberg groups , n > 1

2010 ◽  
Vol 2010 (648) ◽  
Author(s):  
Luca Capogna ◽  
Giovanna Citti ◽  
Maria Manfredini
Keyword(s):  
Heisenberg Groups

Fundamental Solutions of Kohn Sub-Laplacians on Anisotropic Heisenberg Groups and H-type Groups

2011 ◽  
Vol 54 (1) ◽  
pp. 126-140 ◽  
Author(s):  
Yongyang Jin ◽  
Genkai Zhang
Keyword(s):  
Fundamental Solutions ◽  
Meromorphic Continuation ◽  
Heisenberg Groups ◽  
Tempered Distributions

AbstractWe prove that the fundamental solutions of Kohn sub-LaplaciansΔ+iα∂t on the anisotropic Heisenberg groups are tempered distributions and have meromorphic continuation in α with simple poles. We compute the residues and find the partial fundamental solutions at the poles. We also find formulas for the fundamental solutions for some matrix-valued Kohn type sub-Laplacians on H-type groups.

scholarly journals Estimates for Operators Related to the Sub-Laplacian with Drift in Heisenberg Groups

2021 ◽  
Vol 28 (1) ◽  
Author(s):  
Hong-Quan Li ◽  
Peter Sjögren
Keyword(s):  
Heisenberg Group ◽  
Weak Type ◽  
Riesz Transforms ◽  
Heisenberg Groups ◽  
Related Measure

AbstractIn the Heisenberg group of dimension $$2n+1$$ 2 n + 1 , we consider the sub-Laplacian with a drift in the horizontal coordinates. There is a related measure for which this operator is symmetric. The corresponding Riesz transforms are known to be $$L^p$$ L p bounded with respect to this measure. We prove that the Riesz transforms of order 1 are also of weak type (1, 1), and that this is false for order 3 and above. Further, we consider the related maximal Littlewood–Paley–Stein operators and prove the weak type (1, 1) for those of order 1 and disprove it for higher orders.

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