✦ LIBER ✦

Semisimple Orbits of Lie Algebras and Card-Shuffling Measures on Coxeter Groups

✍ Scribed by Jason Fulman

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 119 KB
Volume: 224
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1999.8157

No coin nor oath required. For personal study only.

✦ Synopsis

Random walk on the chambers of hyperplane arrangements is used to define a family of card shuffling measures H W x for a finite Coxeter group W and real x = 0. By algebraic group theory, there is a map from the semisimple orbits of the adjoint action of a finite group of Lie type on its Lie algebra to the conjugacy classes of the Weyl group. Choosing such a semisimple orbit uniformly at random thereby induces a probability measure on the conjugacy classes of the Weyl group. For types A, B, and the identity conjugacy class of W for all types, it is proved that for q very good, this measure on conjugacy classes is equal to the measure arising from H W q . The possibility of refining to a map to elements of the Weyl group is discussed.

📜 SIMILAR VOLUMES

Lp−Lq Estimates for Orbital Measures and

Lp−Lq Estimates for Orbital Measures and Radon Transforms on Compact Lie Groups and Lie Algebras

✍ F. Ricci; G. Travaglini 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 427 KB

Let \(\mu\) be an invariant measure on a regular orbit in a compact Lie group or in a Lie algebra. We prove sharp \(L^{\prime \prime}-L^{4}\) estimates for the convolution operators defined through \(\mu\). We also obtain similar results for the related Radon transform on the Lie algebra. 1945 Acade

On the Surjectivity of the Exponential F

On the Surjectivity of the Exponential Function of Complex Algebraic, Complex Semisimple, and Complex Splittable Lie Groups

✍ Michael Wüstner 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 166 KB

The surjectivity of the exponential function of complex algebraic, in particular of complex semisimple Lie groups, and of complex splittable Lie groups is equivalent to the connectedness of the centralizers of the nilpotent elements in the Lie algebra. This implies that the only complex semisimple L