scholarly journals Cohomology mod $p$ of the 4-connected Cover of the Classifying Space of Simple Lie Groups

2018 ◽  
Author(s):  
Masana Harada ◽  
Akira Kono
Keyword(s):  
Lie Groups ◽  
Classifying Space ◽  
Simple Lie Groups ◽  
Mod P

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 Simple Lie groups stabilizing G-invariant norms

2021 ◽  
Vol 609 ◽  
pp. 308-316
Author(s):  
Marcell Gaál ◽  
Robert M. Guralnick
Keyword(s):  
Lie Groups ◽  
Simple Lie Groups

scholarly journals The index of compact simple Lie groups

2017 ◽  
Vol 49 (5) ◽  
pp. 903-907 ◽  
Author(s):  
Jürgen Berndt ◽  
Carlos Olmos
Keyword(s):  
Lie Groups ◽  
Simple Lie Groups

scholarly journals Flexibility of surface groups in classical simple Lie groups

2015 ◽  
Vol 17 (9) ◽  
pp. 2209-2242
Author(s):  
Inkang Kim ◽  
Pierre Pansu
Keyword(s):  
Lie Groups ◽  
Surface Groups ◽  
Simple Lie Groups

scholarly journals {${\rm Mod}\ p$} decomposition of compact Lie groups

1977 ◽  
Vol 13 (3) ◽  
pp. 627-680 ◽  
Author(s):  
Mamoru Mimura ◽  
Goro Nishida ◽  
Hirosi Toda
Keyword(s):  
Lie Groups ◽  
Compact Lie Groups ◽  
Mod P
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