- Carver Hall 470
- jth@iastate.edu
- jthartwig.net

- Fall 2023
- MATH 301 Abstract Algebra
- Office Hours: MF 11–1 or by appointment

- Past teaching

- Representation theory, Lie algebras, quantum groups
- Invariant theory, Gelfand-Tsetlin theory, Galois orders
- Twisted generalized Weyl algebras, graded rings
- Connections to geometry, integrable systems, mathematical physics

- Organizing Special Session on New Directions in Noncommutative Algebras and Representation Theory at the 2023 Fall Southeastern Sectional Meeting of the AMS at University of South Alabama, Mobile, AL, October 13–15, 2023
- Organized Special Session on Representation Theory, Geometry and Mathematical Physics at the 2023 Spring Central Sectional Meeting of the AMS at University of Cincinnati, Cincinnati, OH, April 15–16, 2023
- Algebra and Geometry Seminar
- The Sioson Collection

- May 5, 2022: Slides and video for my talk
*The Diagonal Reduction Algebra of the Lie Superalgebra 𝖔𝖘𝖕(1|2)*given at Xiamen University, China. - April 8, 2022: Slides for my talk
*Galois Orders and Deformation Quantization*given at the Poisson geometry conference Gone Fishing. - March 26, 2022: Slides for my talk
*On the Diagonal Reduction Algebra of 𝖔𝖘𝖕(1|2)*given in the Special Session on Combinatorics and Representations of Noncommutative Algebras at the Spring Central Sectional Meeting of the AMS. - Oct 5, 2021: Video recording of my talk on the diagonal reduction algebra for the Lie superalgebra 𝖔𝖘𝖕(1|2).
- Jan 26, 2021: Slides for my talk
*Harish-Chandra modules over orders in smash products*at the UTA-KSU Representation Theory and Mathematical Physics Seminar.

Various notes intended for students.

*Locally finite modules over commutative algebras*A quick overview of (generalized) weight modules and (locally) finite-dimensional modules over commutative algebras. These concepts often serve as a basis for representation theory of*noncommutative*algebras which contain a "large" commutative subalgebra.*Highest weight representations of the Virasoro algebra*An introduction to the Virasoro algebra. (This was part of my master's thesis from 2002! My advisor for this part was Arne Meurman.)

- Dylan Fillmore (PhD expected Spring 2024)
- Lillian Uhl (MSc expected Spring 2024)

- Jordan Disch (PhD Spring 2022)
- Dwight Anderson Williams II (Postdoc 2020-2021)
- Fox Hobart (MSc Summer 2021)
- O'Neill Kingston (PhD Spring 2020)
- Erich Jauch (PhD Spring 2020)

*Ghost center and representations of the diagonal reduction algebra of 𝖔𝖘𝖕(1|2)*

with Dwight Anderson Williams II (in Journal of Geometry and Physics)*Grothendieck rings of towers of generalized Weyl algebras in the finite orbit case*

with Daniele Rosso (in Journal of Algebra)

*Diagonal reduction algebra for 𝖔𝖘𝖕(1|2)*

with Dwight Anderson Williams II (in Theoretical and Mathematical Physics)*Harish-Chandra modules over Hopf Galois orders*

(in International Mathematics Research Notices)

*Gelfand-Tsetlin crystals*

with O'Neill Kingston (Preprint)*Grothendieck rings of towers of twisted generalized Weyl algebras*

with Daniele Rosso (in Algebras and Representation Theory)

*Classification of twisted generalized Weyl algebras over polynomial rings*

with Daniele Rosso (in Journal of Algebra)

*Clifford and Weyl superalgebras and spinor representations*

with Vera Serganova (in Transformation Groups)*Simple Whittaker modules over free bosonic orbifold vertex operator algebras*

with Nina Yu (in Proceedings of the AMS)*Dynamical decomposition of bilinear control systems subject to symmetries*

with Domenico D'Alessandro (in Journal of Dynamical and Control Systems)

*Principal Galois orders and Gelfand-Zeitlin modules*

(in Advances in Mathematics)*Unitarizability of weight modules over noncommutative Kleinian fiber products*

(Preprint)

*The q-difference Noether problem for complex reflection groups and quantum OGZ algebras*

(in Communications in Algebra)*Cylindrical Dyck paths and the Mazorchuk-Turowska equation*

with Daniele Rosso (in Journal of Algebraic Combinatorics)*Twisted generalized Weyl algebras and primitive quotients of enveloping algebras*

with Vera Serganova (in Algebras and Representation Theory)

*Quantum affine modules for non-twisted affine Kac-Moody algebras*

with Vyacheslav Futorny and Evan Wilson (in Proceedings of the AMS)*The isomorphism problem for multiparameter quantized Weyl algebras*

with Ken Goodearl (in São Paulo Journal of Mathemaical Sciences)*Irreducible completely pointed modules for quantum groups of type A*

with Vyacheslav Futorny and Evan Wilson (in Journal of Algebra)

*De Concini-Kac filtration and Gelfand-Tsetlin generators for quantum gl*_{N}

with Vyacheslav Futorny (in Linear Algebra and its Applications)

*Solution to a q-difference Noether problem and the quantum Gelfand-Kirillov conjecture for gl*_{N}

with Vyacheslav Futorny (in Mathematische Zeitschrift)*Extended trigonometric Cherednik algebras and nonstationary Schrödinger equations with delta-potentials*

with Jasper Stokman (in Journal of Mathematical Physics)*Multiparameter twisted Weyl algebras*

with Vyacheslav Futorny (in Journal of Algebra)*On the consistency of twisted generalized Weyl algebras*

with Vyacheslav Futorny (in Proceedings of the AMS)

*Simplicity and maximal commutative subalgebras of twisted generalized Weyl algebras*

with Johan Öinert (in Journal of Algebra)

*Twisted generalized Weyl algebras, polynomial Cartan matrices and Serre-type relations*

(in Communications in Algebra)

*The elliptic GL(n) dynamical quantum group as an 𝖍-Hopf algebroid*

(in International Journal of Mathematics and Mathematical Sciences)*Pseudo-unitarizable weight modules over generalized Weyl algebras*

(in Journal of Pure and Applied Algebra)

*Hopf structures on ambiskew polynomial rings*

(in Journal of Pure and Applied Algebra)*Locally finite simple weight modules over twisted generalized Weyl algebras*

(in Journal of Algebra)

*Deformations of Lie algebras using σ-derivations*

with Daniel Larsson and Sergei Silvestrov (in Journal of Algebra)

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