scholarly journals Pointwise estimates of the size of characters of compact Lie groups

2000 ◽  
Vol 69 (1) ◽  
pp. 61-84 ◽  
Author(s):  
Kathryn E. Hare ◽  
David C. Wilson ◽  
Wai Ling Yee
Keyword(s):  
Lie Groups ◽  
Classical Result ◽  
Pointwise Estimates ◽  
Compact Lie Groups ◽  
Simple Lie Groups ◽  
Orbital Measure ◽  
Continuous Measures ◽  
Minimal Integer

AbstractPointwise bounds for characters of representations of the classical, compact, connected, simple Lie groups are obtained with which allow us to study the singularity of central measures. For example, we find the minimal integer k such that any continuous orbital measure convolved with itself k times belongs to L2. We also prove that if k = rank G then μ 2k ∈ L1 for all central, continuous measures μ. This improves upon the known classical result which required the exponent to be dimension of the group G.

The Betti Numbers of the Simple Lie Groups

1958 ◽  
Vol 10 ◽  
pp. 349-356 ◽  
Author(s):  
A. J. Coleman
Keyword(s):  
Lie Groups ◽  
Orthogonal Group ◽  
Betti Numbers ◽  
Algebraic Methods ◽  
Classical Groups ◽  
Compact Lie Groups ◽  
Poincaré Polynomial ◽  
Unimodular Group ◽  
Simple Lie Groups

The purpose of the present paper1 is to simplify the calculation of the Betti numbers of the simple compact Lie groups. For the unimodular group and the orthogonal group on a space of odd dimension the form of the Poincaré polynomial was correctly guessed by E. Cartan in 1929 (5, p. 183). The proof of his conjecture and its extension to the four classes of classical groups was given by L. Pontrjagin (13) using topological arguments and then by R. Brauer (2) using algebraic methods.

scholarly journals The size of characters of exceptional lie groups

2004 ◽  
Vol 77 (2) ◽  
pp. 233-248 ◽  
Author(s):  
Kathryn E. Hare ◽  
Karen Yeats
Keyword(s):  
Lie Groups ◽  
Classical Result ◽  
Continuous Measure ◽  
Compact Lie Groups ◽  
Absolutely Continuous ◽  
Exceptional Lie Groups

AbstractPointwise bounds for characters of representations of the compact, connected, simple, exceptional Life groups are obtained. It is a classical result that if μ is a central, continuous measure on such a group, then μdimG is absolutely continuous. Our estimates on the size of characters allow us to prove that the exponent, dimension of G, can be replaced by approximately the rank of G. Similar results were obtained earlier for the classical, compact Lie groups.

Pointwise estimates for some kernels on compact Lie groups

1982 ◽  
Vol 31 (2) ◽  
pp. 145-158 ◽  
Author(s):  
Michael Cowling ◽  
Anna Maria Mantero ◽  
Fulvio Ricci
Keyword(s):  
Lie Groups ◽  
Pointwise Estimates ◽  
Compact Lie Groups

scholarly journals On the Non-Commutativity of Pontrjagin Rings Mod 3 of Some Compact Exceptional Groups

1960 ◽  
Vol 17 ◽  
pp. 225-260 ◽  
Author(s):  
Shôrô Araki
Keyword(s):  
Lie Groups ◽  
Rational Numbers ◽  
Compact Lie Groups ◽  
Graded Algebras ◽  
Exceptional Groups ◽  
Simple Lie Groups

Pontrjagin rings over the field of rational numbers of compact Lie groups are commutative in the sense of graded algebras (or anti-commutative in the classical terminology) [14]. Pontrjagin rings over the field Zp (p 0) of several compact simple Lie groups were studied by Borel [5]. The most examples are commutative. However, this is generally not true.

scholarly journals Continuous measures on compact Lie groups

2000 ◽  
Vol 50 (4) ◽  
pp. 1277-1296 ◽  
Author(s):  
M. Anoussis ◽  
A. Bisbas
Keyword(s):  
Lie Groups ◽  
Compact Lie Groups ◽  
Continuous Measures

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.

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