Isomorphisms of the Integral Classical Groups and Their Congruence Subgroups

1975 ◽  
Vol 97 (4) ◽  
pp. 865 ◽  
Author(s):  
Alexander J. Hahn
Keyword(s):  
Classical Groups ◽  
Congruence Subgroups

scholarly journals Local-global principle for congruence subgroups of Chevalley groups

2014 ◽  
Vol 12 (6) ◽  
Author(s):  
Himanee Apte ◽  
Alexei Stepanov
Keyword(s):  
Polynomial Ring ◽  
Principal Congruence ◽  
Classical Groups ◽  
Reductive Groups ◽  
Congruence Subgroups ◽  
Chevalley Groups ◽  
Common Generalization ◽  
Independent Variable ◽  
The Absolute ◽  
Global Principle

AbstractSuslin’s local-global principle asserts that if a matrix over a polynomial ring vanishes modulo the independent variable and is locally elementary then it is elementary. In this article we prove Suslin’s local-global principle for principal congruence subgroups of Chevalley groups. This result is a common generalization of the result of Abe for the absolute case and Apte, Chattopadhyay and Rao for classical groups. For the absolute case the localglobal principle was recently obtained by Petrov and Stavrova in the more general settings of isotropic reductive groups.

Classical Groups, Derangements and Primes

2015 ◽  
Author(s):  
Timothy C. Burness ◽  
Michael Giudici
Keyword(s):  
Classical Groups

scholarly journals Twisted 6d (2, 0) SCFTs on a circle

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Zhihao Duan ◽  
Kimyeong Lee ◽  
June Nahmgoong ◽  
Xin Wang
Keyword(s):  
Lie Groups ◽  
Point Of View ◽  
Partition Functions ◽  
Congruence Subgroups ◽  
Gauge Groups ◽  
Simple Lie Groups ◽  
Instanton Contribution ◽  
Elliptic Genera ◽  
Supersymmetric Gauge ◽  
The One

Abstract We study twisted circle compactification of 6d (2, 0) SCFTs to 5d $$ \mathcal{N} $$ N = 2 supersymmetric gauge theories with non-simply-laced gauge groups. We provide two complementary approaches towards the BPS partition functions, reflecting the 5d and 6d point of view respectively. The first is based on the blowup equations for the instanton partition function, from which in particular we determine explicitly the one-instanton contribution for all simple Lie groups. The second is based on the modular bootstrap program, and we propose a novel modular ansatz for the twisted elliptic genera that transform under the congruence subgroups Γ0(N) of SL(2, ℤ). We conjecture a vanishing bound for the refined Gopakumar-Vafa invariants of the genus one fibered Calabi-Yau threefolds, upon which one can determine the twisted elliptic genera recursively. We use our results to obtain the 6d Cardy formulas and find universal behaviour for all simple Lie groups. In addition, the Cardy formulas remain invariant under the twist once the normalization of the compact circle is taken into account.

scholarly journals TOPOLOGICAL NOETHERIANITY FOR ALGEBRAIC REPRESENTATIONS OF INFINITE RANK CLASSICAL GROUPS

2021 ◽  
Author(s):  
R. H. EGGERMONT ◽  
A. SNOWDEN
Keyword(s):  
Classical Groups ◽  
Infinite Rank ◽  
Polynomial Representations ◽  
Algebraic Representations

AbstractDraisma recently proved that polynomial representations of GL∞ are topologically noetherian. We generalize this result to algebraic representations of infinite rank classical groups.

scholarly journals On some automorphic properties of Galois traces of class invariants from generalized Weber functions of level 5

2019 ◽  
Vol 17 (1) ◽  
pp. 1631-1651
Author(s):  
Ick Sun Eum ◽  
Ho Yun Jung
Keyword(s):  
Modular Forms ◽  
Fourier Coefficients ◽  
Singular Values ◽  
Congruence Subgroups ◽  
Maass Form ◽  
Weakly Holomorphic Modular Forms ◽  
Reciprocity Law ◽  
Class Invariants ◽  
Higher Genus ◽  
Holomorphic Modular Forms

Abstract After the significant work of Zagier on the traces of singular moduli, Jeon, Kang and Kim showed that the Galois traces of real-valued class invariants given in terms of the singular values of the classical Weber functions can be identified with the Fourier coefficients of weakly holomorphic modular forms of weight 3/2 on the congruence subgroups of higher genus by using the Bruinier-Funke modular traces. Extending their work, we construct real-valued class invariants by using the singular values of the generalized Weber functions of level 5 and prove that their Galois traces are Fourier coefficients of a harmonic weak Maass form of weight 3/2 by using Shimura’s reciprocity law.

scholarly journals Power series coefficients for probabilities in finite classical groups

2006 ◽  
Vol 305 (2) ◽  
pp. 1212-1237
Author(s):  
John R. Britnell ◽  
Jason Fulman
Keyword(s):  
Power Series ◽  
Classical Groups ◽  
Finite Classical Groups

scholarly journals Minimal logarithmic signatures for one type of classical groups

2016 ◽  
Vol 28 (2) ◽  
pp. 177-192
Author(s):  
Haibo Hong ◽  
Licheng Wang ◽  
Haseeb Ahmad ◽  
Jun Shao ◽  
Yixian Yang
Keyword(s):  
Classical Groups ◽  
Logarithmic Signatures
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