Algebraic Monoids, Group Embeddings, and Algebraic Combinatorics

✍ Scribed by Mahir Can, Zhenheng Li, Benjamin Steinberg, Qiang Wang (eds.)

• Publisher: Springer-Verlag New York
• Year: 2014
• Tongue: English
• Leaves: 360
• Series: Fields Institute Communications 71
• Edition: 1
• Category: Library

✦ Synopsis

This book contains a collection of fifteen articles and is dedicated to the sixtieth birthdays of Lex Renner and Mohan Putcha, the pioneers of the field of algebraic monoids.

Topics presented include:

structure and representation theory of reductive algebraic monoids

monoid schemes and applications of monoids

monoids related to Lie theory

equivariant embeddings of algebraic groups

constructions and properties of monoids from algebraic combinatorics

endomorphism monoids induced from vector bundles

Hodge–Newton decompositions of reductive monoids

A portion of these articles are designed to serve as a self-contained introduction to these topics, while the remaining contributions are research articles containing previously unpublished results, which are sure to become very influential for future work. Among these, for example, the important recent work of Michel Brion and Lex Renner showing that the algebraic semi groups are strongly π-regular.

Graduate students as well as researchers working in the fields of algebraic (semi)group theory, algebraic combinatorics and the theory of algebraic group embeddings will benefit from this unique and broad compilation of some fundamental results in (semi)group theory, algebraic group embeddings and algebraic combinatorics merged under the umbrella of algebraic monoids.

✦ Table of Contents

Front Matter....Pages i-x
On Algebraic Semigroups and Monoids....Pages 1-54
Algebraic Semigroups Are Strongly π -Regular....Pages 55-59
Rees Theorem and Quotients in Linear Algebraic Semigroups....Pages 61-86
Representations of Reductive Normal Algebraic Monoids....Pages 87-96
On Linear Hodge Newton Decomposition for Reductive Monoids....Pages 97-118
The Structure of Affine Algebraic Monoids in Terms of Kernel Data....Pages 119-140
Algebraic Monoids and Renner Monoids....Pages 141-187
Conjugacy Decomposition of Canonical and Dual Canonical Monoids....Pages 189-208
The Endomorphisms Monoid of a Homogeneous Vector Bundle....Pages 209-231
On Certain Semigroups Derived from Associative Algebras....Pages 233-245
The Betti Numbers of Simple Embeddings....Pages 247-269
SL 2 -Regular Subvarieties of Complete Quadrics....Pages 271-284
Markov Chains for Promotion Operators....Pages 285-304
Fomin-Greene Monoids and Pieri Operations....Pages 305-338
Affine Permutations and an Affine Catalan Monoid....Pages 339-354

✦ Subjects

Combinatorics; Group Theory and Generalizations; Topological Groups, Lie Groups; Algebraic Geometry