#### 1,937 Citations

Lectures on Lie Groups

- Mathematics
- 1998

Linear groups and linear representations Lie groups and Lie algebras orbital geometry of the adjoint action coxeter groups, Weyl reduction and Weyl formulas structural theory of compact Lie algebras… Expand

Heinz-Kato’s Inequalities for Lie Groups

- 2009

Extensions of Heinz-Kato’s inequalities and related inequalities are obtained for semisimple connected noncompact Lie groups. Mathematics Subject Index 2000:Primary 22E46; Secondary 15A45.

Notes on Integration on Lie Groups

- 2013

This is a very informal set of notes on integration on Lie groups and connections with basic representation theory. We give some constructions of the Lie group integral, show how some integrals can… Expand

Heinz-Kato's inequalities for semisimple Lie groups

- Mathematics
- 2009

Extensions of Heinz-Kato's inequalities and related inequalities are obtained for semisimple connected noncompact Lie groups.

Cohomology of Jordan triples and Lie algebras

- 2014

We develop a cohomology theory for Jordan triples, including the infinite dimensional ones, by means of the cohomology of TKK Lie algebras. This enables us to apply Lie cohomological results to the… Expand

Surjectivity of power maps of real algebraic groups

- Mathematics
- 2011

Abstract In this paper we study the surjectivity of the power maps g ↦ g n for real points of algebraic groups defined over reals. The results are also applied to study the exponentiality of such… Expand

Simple Roots and Weyl Groups

- Mathematics
- 2016

Its origins in the theory of Lie algebras are introduced, and then an axiomatic definition is provided. Simple roots, Bases, Weyl groups, and the transitive action of the latter on the former are… Expand

LECTURES ON THE GEOMETRY AND MODULAR REPRESENTATION THEORY OF ALGEBRAIC GROUPS

- Mathematics
- Journal of the Australian Mathematical Society
- 2021

Abstract These notes provide a concise introduction to the representation theory of reductive algebraic groups in positive characteristic, with an emphasis on Lusztig's character formula and… Expand

On the Homomorphisms of the Lie Groups SU ( 2 ) and S 3

- 2014

and Applied Analysis 3 For the second set of the solutions, φ is of the following form: φ (V 1 ) = aU 2 + bU 3 ,

The cohomology of locally analytic representations

- Mathematics
- 2010

Abstract We develop a cohomology theory for locally analytic representations of p-adic Lie groups on nonarchimedean locally convex vector spaces. There are versions of Pontrjagin duality, Shapiro's… Expand