Georgia Benkart's Books

Volume 197, number 920 (second of 5 numbers).

Introduction The $\mathfrak{g}$-module decomposition of a $\mathrm{BC}_r$-graded Lie algebra, $r\ge 3$ (excluding type $\mathrm{D}_3)$ Models for $\mathrm{BC}_r$-graded Lie algebras, $r\ge 3$ (excluding type $\mathrm{D}_3)$ The $\mathfrak{g}$-module decomposition of a $\mathrm{BC}_r$-graded Lie algebra with grading subalgebra of type $\mathrm{B}_2$, $\mathrm{C}_2$, $\mathrm{D}_2$, or $\mathrm{D}_3$ Central extensions, derivations and invariant forms Models of $\mathrm{BC}_r$-graded Lie algebras with grading subalgebra of type $\mathrm{B}_2$, $\mathrm{C}_2$, $\mathrm{D}_2$, or $\mathrm{D}_3$ Appendix: Peirce decompositions in structurable algebras References.

In this work we consider the problem of determining information about representations as the rank grows large, in fact, tends to infinity. Here we show that the set of dominant weights stabilizes as the rank goes to infinity and the multiplicities become polynomials in the rank. In addition, we give effective, easily computable algorithms for determining the set of dominant weights and illustrate how to calculate their multiplicity polynomials.

Discusses the problem of determining the finite-dimensional simple Lie algebras over an algebraically closed field of characteristic $p>7$. This book includes topics such as Lie algebras of prime characteristic, algebraic groups, combinatorics and representation theory, and Kac-Moody and Virasoro algebras.

Book's by Georgia Benkart

The Recognition Theorem for Graded Lie Algebras in Prime Characteristic

The Recognition Theorem for Graded Lie Algebras in Prime Characteristic

Lie Algebras Graded by the Root Systems BC$_r$, $r\geq 2$

Lie Algebras Graded by the Root Systems BC$_r$, $r\geq 2$

Stability in Modules for Classical Lie Algebras: A Constructive Approach

Stability in Modules for Classical Lie Algebras: A Constructive Approach

Lie Algebras and Related Topics

Lie Algebras and Related Topics

Stability in Modules for Classical Lie Algebras: A Constructive Approach

Stability in Modules for Classical Lie Algebras: A Constructive Approach

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