Research

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My research interests include representation theory and algebraic combinatorics, with a focus on the following topics:

  • Representation theory of symmetric groups and Lie algebras.
  • Crystals and combinatorics of quantum groups.
  • Categorification and diagrammatic algebra.

Papers:

  1. C. Bowman, Z. Daugherty, M. De Visscher, R. Muth, L. Poulain D’andecy, The orientifold Temperley–Lieb algebra, (2025), arXiv
  2. N. Davidson, J. Kujawa and R. Muth, Superalgebra deformations of web categories: Affine and cyclotomic webs, (2025), (submitted), arXiv
  3. C. Bowman, R. Muth, L. Speyer and L. Sutton, Morita equivalences between cyclotomic KLR algebras in types 𝙲∞{\tt C}_{\infty} and 𝙰∞{\tt A}_{\infty}, (2025), (submitted), arXiv
  4. R. Muth, T. Nicewicz, L. Speyer and L. Sutton, A skew Specht perspective of RoCK blocks and cuspidal systems for KLR algebras in affine type A, Representation Theory 29 (2025), 70 pp., https://doi.org/10.1090/ert/698, arXiv
  5. C. Bowman, M. De Visscher, A. Dell’Arciprete, A. Hazi, R. Muth and C. Stroppel, Faithful covers of Khovanov arc algebras, Mathematische Zeitschrift (to appear) (2025) arXiv
  6. C. Bowman, M. De Visscher, A. Dell’Arciprete, A. Hazi, R. Muth and C. Stroppel, Quiver presentations and Schur-Weyl duality for Khovanov arc algebras, (2024), (submitted), arXiv
  7. N. Davidson, J. R. Kujawa and R. Muth, Howe Duality of Type P, Transformation Groups (2024), 46 pp., https://doi.org/10.1007/s00031-024-09850-7, arXiv
  8. N. Davidson, J. R. Kujawa and R. Muth, Webs of Type P, Canadian Journal of Mathematics (2023), 41pp., https://doi.org/10.4153/S0008414X23000688, arXiv
  9. N. Davidson, J. R. Kujawa, R. Muth and J. Zhu, Superalgebra deformations of web categories: finite webs, (2023), 64 pp., (submitted), arXiv
  10. D. Abbasian, L. Difulvio, R. Muth, G. Pasternak, I. Sholtes and F. Sinclair, Cuspidal ribbon tableaux in affine type A, Algebraic Combinatorics 6(2) (2023), 34 pp., https://doi.org/10.5802/alco.260, arXiv
  11. A. Kleshchev and R. Muth, Schurifying quasi-hereditary algebras, Proceedings of the London Mathematical Society 125 (2022), 54pp., https://doi.org/10.1112/plms.12466, arXiv
  12. R. Muth, L. Speyer and L. Sutton, Decomposable Specht modules indexed by bihooks II, Algebras and Representation Theory 26 (2021), 40pp., https://doi.org/10.1007/s10468-021-10093-3, arXiv
  13. A. Kleshchev and R. Muth, Based quasi-hereditary algebras, Journal of Algebra 558 (2020), 18 pp., https://doi.org/10.1016/j.jalgebra.2019.04.034, arXiv
  14. A. Kleshchev and R. Muth, Generalized Schur algebras, Algebra & Number Theory 14 (2020), 44 pp., https://doi.org/10.2140/ant.2020.14.501, arXiv
  15. R. Muth, Super RSK correspondence with symmetry, Electronic Journal of Combinatorics 26(2) (2019), #P2.27, 26 pp., https://doi.org/10.37236/8150, arXiv
  16. A. Kleshchev and R. Muth, Affine zigzag algebras and imaginary strata for KLR algebras, Transactions of the American Mathematical Society 371 (2019), 44 pp., https://doi.org/10.1090/tran/7464, arXiv
  17. R. Muth, Graded skew Specht modules and cuspidal modules for Khovanov-Lauda-Rouquier algebras of affine type A, Algebras and Representation Theory 22 (2018), 32 pp., https://doi.org/10.1007/s10468-018-9808-2, arXiv
  18. A. Kleshchev and R. Muth, Stratifying KLR algebras of affine ADE types, Journal of Algebra 475 (2017), 37 pp., https://doi.org/10.1016/j.jalgebra.2016.07.006, arXiv
  19. A. Kleshchev and R. Muth, Imaginary Schur-Weyl duality, Memoirs of the American Mathematical Society 245 (2017), no. 1157, xvii, 83 pp., arXiv

With undergraduates:

  1. R. Eisel, V. McMullen and R. Muth, An efficient search strategy for hidden ideals in pointed partially ordered sets, Journal of Combinatorial Mathematics and Combinatorial Computing 128 (2025), 17 pp., https://doi.org/10.61091/jcmcc128-11, arXiv
  2. D. Denniston, R. Muth and V. Singh, The configuration space of a robotic arm over a graph, Discrete Mathematics, Algorithms and Applications, 15(7) (2023), 20pp., https://doi.org/10.1142/S1793830922501506, arXiv
  3. T. Einolf, R. Muth and J. Wilkinson, Injectively k-colored rooted forests, Graphs and Combinatorics 39 (2023), 33pp., https://doi.org/10.1007/s00373-023-02700-5, arXiv
  4. A. Iams, H. Johnston and R. Muth, Searching for quicksand ideals in partially ordered sets, Australasian Journal of Combinatorics 79(2) (2021), 27 pp., https://ajc.maths.uq.edu.au/pdf/79/ajc_v79_p256.pdf, arXiv
  5. D. Florentino, E. Moy and R. Muth, Cooperative half-guards in art galleries, (2020), 16 pp., arXiv