Emilie Wiesner

WHITTAKER MODULES FOR THE VIRASORO ALGEBRA

Whittaker modules have been well studied in the setting of complex semisimple Lie algebras. Their definition can easily be generalized to certain other Lie algebras with triangular decomposition, including the Virasoro algebra. We define Whittaker modules for the Virasoro algebra and obtain analogues to several results from the classical setting, including a classification of simple Whittaker modules by central characters and composition series for general Whittaker modules.

Simple Virasoro modules induced from codimension one subalgebras of the positive part

We construct a new five-parameter family of simple modules over the Virasoro Lie algebra.

Whittaker Categories for the Virasoro Algebra

This article builds on work from [16], where the authors described Whittaker modules for the Virasoro algebra. Using the framework outlined in [3], the current article investigates a category of Virasoro-algebra modules that includes Whittaker modules. Results in this article include a classification of the simple modules in the category and a description of certain induced modules that are a natural generalization of simple Whittaker modules.

Using Informal Inferential Reasoning to Develop Formal Concepts: Analyzing an Activity

Inferential reasoning is a central component of statistics. Researchers have suggested that students should develop an informal understanding of the ideas that underlie inference before learning the concepts formally. This paper presents a hands-on activity that is designed to help students in an introductory statistics course draw informal inferences about a bag of bingo chips and connect these ideas to the formal T-test and confidence interval. This activity is analyzed using a framework and recommendations drawn from the research literature.

Whittaker Categories and Whittaker Modules for Lie Superalgebras

Following analogous constructions for Lie algebras, we define Whittaker modules and Whittaker categories for finite-dimensional simple Lie superalgebras. Results include a decomposition of Whittaker categories for a Lie superalgebra according to the action of an appropriate sub-superalgebra; and, for basic classical Lie superalgebras of type I, the construction of Whittaker modules from Whittaker modules for the even part.

Automorphisms and Derivations of the Insertion–Elimination Algebra and Related Graded Lie Algebras

This paper addresses several structural aspects of the insertion–elimination algebra

Chapter 3 – Adaptation and Fitness Graphs

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Undergraduate Students' Self-Reported Use of Mathematics Textbooks

g, a Lie algebra that can be realized in terms of tree-inserting and tree-eliminating operations on the set of rooted trees. In particular, we determine the finite-dimensional subalgebras of