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

- Spring 2023
- MATH 505 Abstract Algebra II
- Office Hours: M 1–2, 4–5; T 3–4(Webex); W 2–3; Th 9:30–11; and 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 a Special Session on Representation Theory, Geometry and Mathematical Physics at the 2023 Spring Central Sectional Meeting 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)

- 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 (Preprint)

*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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