Publications: Stephen R Doty

Preprints

  1. (with Anthony Giaquinto) Origins of the Temperley-Lieb algebra: early history. Preprint 2023, arXiv:2307.11929

Published

  1. (with Chris Bowman and Stuart Martin) Canonical bases and new applications of increasing and decreasing subsequences to invariant theory. J. Algebra 659, 23–43 (2024).

  2. (with Anthony Giaquinto) Schur-Weyl duality for twin groups. Transform. Groups 29, no. 2, 621–645 (2024).

  3. (with Anthony Giaquinto) An orthogonal realization of representations of the Temperley-Lieb algebra. J. Algebra 655, 294–332 (2024).

  4. (with Anthony Giaquinto) The partial Temperley–Lieb algebra and its representations. J. Comb. Algebra 7 no. 3/4, 401–439 (2023).

  5. Doubly stochastic matrices and Schur-Weyl duality for partition algebras. Electronic J. of Combinatorics 29(4) (2022), Article No. P4.28.

  6. (with Chris Bowman and Stuart Martin) Integral Schur-Weyl duality for partition algebras. Algebraic Combinatorics 5, 371–399 (2022).

  7. (with Chris Bowman and Stuart Martin) An integral second fundamental theorem of invariant theory for partition algebras. Represent. Theory 26, 437–454 (2022).

  8. (with Anthony Giaguinto) Schur-Weyl duality for tensor powers of the Burau representation. Res. Math. Sci. 8, No. 47 (2021).

  9. (with Aaron Lauve and George Seelinger) Canonical idempotents of multiplicity-free families of algebras. Enseign. Math. 64, 23–63 (2019).

  10. (with J. Matthew Douglass) Schur-Weyl duality and the free Lie algebra. Proc. Amer. Math. Soc. 145, 3263–3277 (2017). See Errata.

  11. (with Anthony Giaquinto) Cellular bases of generalised q-Schur algebras. Math. Proc. Camb. Philos. Soc. 162, 533–560 (2017).

  12. (with Chris Bowman and Stuart Martin) Decomposition of tensor products of modular irreducible representations for SL3: the p ≥ 5 case. Int. Electron. J. Algebra. 17, 105–138 (2015).

  13. Representations of reductive normal algebraic monoids. In: Can, M., Li, Z., Steinberg, B., and Wang, Q. (eds.) Algebraic Monoids, Group Embeddings, and Algebraic Combinatorics. pp. 87–96. Springer New York, New York, NY (2014).

  14. (with Yiqiang Li) A geometric construction of generalized q-Schur algebras. In: Achar, P., Jakelić, D., Misra, K., and Yakimov, M. (eds.) Contemp. Math. 623, pp. 55–62. Amer. Math. Soc., Providence, RI (2014).

  15. (with Richard Dipper and Friederike Stoll) The quantized walled Brauer algebra and mixed tensor space. Algebr. Represent. Theory. 17, 675–701 (2014).

  16. (with Richard Dipper and Friederike Stoll) Quantized mixed tensor space and Schur–Weyl duality. Algebra Number Theory. 7, 1121–1146 (2013).

  17. A characteristic-free decomposition of tensor space as a Brauer algebra module. J. Lie Theory. 22, 869–882 (2012).

  18. (with Katherine Nyman) Annihilators of permutation modules. Q. J. Math. 62, 87–102 (2011).

  19. (with Chris Bowman and Stuart Martin) Decomposition of tensor products of modular irreducible representations for SL3. With an appendix by C.M. Ringel. Int. Electron. J. Algebra. 9, 177–219 (2011).

  20. Addendum to “Constructing quantized enveloping algebras via inverse limits of finite dimensional algebras” [J. Algebra 321 (4) (2009) 1225–1238]. J. Algebra. 323, 1845–1847 (2010).

  21. Factoring tilting modules for algebraic groups. J. Lie Theory. 19, 531–535 (2009).

  22. (with David J. Benson) Schur–Weyl duality over finite fields. Arch. Math. 93, 425–435 (2009). See Errata.

  23. Schur-Weyl duality in positive characteristic. In: Lin, Z. and Wang, J. (eds.) Contemp. Math. 478, pp. 15–28. Amer. Math, Soc., Providence, RI (2009).

  24. (with Anthony Giaquinto and John B. Sullivan) On the defining relations for generalized q-Schur algebras. Adv. Math. 221, 955–982 (2009).

  25. (with Jun Hu) Schur-Weyl duality for orthogonal groups. Proc. Lond. Math. Soc. (3). 98, 679–713 (2009).

  26. (with Stuart Martin) Hook modules for general linear groups. Arch. Math. 92, 206–214 (2009).

  27. Constructing quantized enveloping algebras via inverse limits of finite dimensional algebras. J. Algebra. 321, 1225–1238 (2009).

  28. (with Anton Cox, Maud De Visscher, and Paul P. Martin) On the blocks of the walled Brauer algebra. J. Algebra. 320, 169–212 (2008).

  29. (with Richard Dipper) The rational Schur algebra. Represent. Theory. 12, 58–83 (2008). See Errata.

  30. (with Richard Dipper and Jun Hu) Brauer algebras, symplectic Schur algebras and Schur-Weyl duality. Trans. Amer. Math. Soc. 360, 189–214 (2008).

  31. (with R.M. Green) Presenting affine q-Schur algebras. Math. Z. 256, 311–345 (2007).

  32. (with Karin Erdmann and Anne Henke) Endomorphism rings of permutation modules over maximal Young subgroups. J. Algebra. 307, 377–396 (2007).

  33. (with Anthony Giaquinto, and John B. Sullivan) Presenting generalized Schur algebras in types B, C, D. Adv. Math. 206, 434–454 (2006).

  34. (with Anne Henke) Decomposition of tensor products of modular irreducibles for SL2. Q. J. Math. 56, 189–207 (2005).

  35. New versions of Schur-Weyl duality. In: Finite Groups 2003. pp. 59–71. Walter de Gruyter, Berlin (2004).

  36. (with Karin Erdmann and Anne Henke) A generic algebra associated to certain Hecke algebras. J. Algebra. 278, 502–531 (2004).

  37. (with Karin Erdmann and Daniel K. Nakano) Extensions of modules over Schur algebras, symmetric groups and Hecke algebras. Algebr. Represent. Theory. 7, 67–99 (2004).

  38. (with Anthony Giaquinto) Presenting Schur algebras as quotients of the universal enveloping algebra of 𝔤𝔩2. Algebr. Represent. Theory. 7, 1–17 (2004).

  39. Presenting generalized q-Schur algebras. Represent. Theory. 7, 196–213 (2003). See Errata.

  40. (with Georgia Benkart) Derangements and tensor powers of adjoint modules for 𝔰𝔩n. J. Algebraic Combin. 16, 31–42 (2002). See Errata.

  41. (with Anthony Giaquinto) Presenting Schur algebras. Internat. Math. Res. Notices. 2002, 1907 (2002). See Errata.

  42. (with Daniel K. Nakano) Relating the cohomology of general linear groups and symmetric groups. In: Modular Representation Theory of Finite Groups. pp. 175–187. de Gruyter, Berlin (2001).

  43. (with Anthony Giaquinto) Generators and relations for Schur algebras. Electron. Res. Announc. Amer. Math. Soc. 7, 54–62 (2001).

  44. (with Karin Erdmann, Stuart Martin, and Daniel K. Nakano) Representation type of Schur algebras. Math Z. 232, 137–182 (1999). See Errata.

  45. Representation theory of reductive normal algebraic monoids. Trans. Amer. Math. Soc. 351, 2539–2551 (1999).

  46. (with Daniel K. Nakano) Semisimple Schur Algebras. Math. Proc. Camb. Philos. Soc. 124, 15–20 (1998).

  47. Polynomial representations, algebraic monoids, and Schur algebras of classical type. J. Pure Appl. Algebra. 123, 165–199 (1998).

  48. (with Daniel K. Nakano and Karl M. Peters) Infinitesimal Schur algebras of finite representation type. Q. J. Math. 48, 323–345 (1997).

  49. (with Daniel K. Nakano and Karl M. Peters) Polynomial representations of Frobenius kernels of GL2. In: Kang, S.-J., Kim, M.-H., and Lee, I. (eds.) Contemp. Math. 194, pp. 57–67. Amer. Math. Soc., Providence, RI (1996).

  50. (with Daniel K. Nakano and Karl M. Peters) On infinitesimal Schur algebras. Proc. London Math. Soc. (3) 72, 588–612 (1996).

  51. (with Grant Walker) Truncated symmetric powers and modular representations of GLn. Math. Proc. Camb. Philos. Soc. 119, 231–242 (1996).

  52. Resolutions of B modules. Indag. Math. (N.S.) 5, 267–283 (1994).

  53. (with Grant Walker) Modular symmetric functions and irreducible modular representations of general linear groups. J. Pure Appl. Algebra. 82, 1–26 (1992).

  54. (with Grant Walker) The composition factors of Fp[x1, x2, x3] as a GL(3, p)-module. J. Algebra. 147, 411–441 (1992).

  55. The symmetric algebra and representations of general linear groups. In: Proceedings of the Hyderabad Conference on Algebraic Groups (Hyderabad, 1989). pp. 123–150. Manoj Prakashan, Madras (1991).

  56. Filtrations of rational representations of reductive groups of semisimple rank 1. Proc. Amer. Math. Soc. 109, 9–22 (1990).

  57. Character formulas and Frobenius subgroups of algebraic groups. J. Algebra. 125, 331–347 (1989).

  58. Submodules of symmetric powers of the natural module for 𝐺𝐿𝑛. In: Fossum, R., Haboush, W., Hochster, M., and Lakshmibai, V. (eds.) Contemp. Math. 88, pp. 185–191. Amer. Math. Soc., Providence, RI (1989).

  59. The strong linkage principle. Amer. J. Math. 111, 135–141 (1989).

  60. (with John B. Sullivan) On the intertwinings between higher cohomology modules of line bundles on G/B. J. Algebra. 115, 289–296 (1988).

  61. (with John B. Sullivan) On the structure of the higher cohomology modules of line bundles on G/B. J. Algebra. 114, 286–332 (1988).

  62. (with John B. Sullivan) Filtration patterns for representations of algebraic groups and their Frobenius Kernels. Math Z. 195, 391–407 (1987).

  63. (with John B. Sullivan) On the geometry of extensions of irreducible modules for simple algebraic groups. Pacific J. Math. 130, 253–273 (1987).

  64. Composition factors of induced modules for algebraic groups and their Frobenius subgroups. In: The Arcata Conference on Representations of Finite Groups (Arcata, Calif., 1986). pp. 163–170. Amer. Math. Soc., Providence, RI (1987).

  65. (with John B. Sullivan) The submodule structure of Weyl modules for SL3. J. Algebra. 96, 78–93 (1985).

  66. The submodule structure of certain Weyl modules for groups of type An. J. Algebra. 95, 373–383 (1985).

  67. The Submodule Structure of Weyl Modules for Groups of Type An. Ph.D. Thesis — University of Notre Dame, ProQuest LLC, Ann Arbor, MI (1982).