Publications of S. R. Doty

Dissertation

The Submodule Structure of Weyl Modules for Groups of Type An, University of Notre Dame, 1982.

Research Articles

  1. Doty, Stephen R., The submodule structure of certain Weyl modules for groups of type An, J. Algebra 95 (1985), no. 2, 373–383.
  2. Doty, Stephen R.; Sullivan, John B., The submodule structure of Weyl modules for SL3, J. Algebra 96 (1985), no. 1, 78–93.
  3. Doty, Stephen R.; Sullivan, John B., On the structure of the higher cohomology modules of line bundles on G∕B, J. Algebra 114 (1988), no. 2, 286–332.
  4. Doty, Stephen R.; Sullivan, John B, On the geometry of extensions of irreducible modules for simple algebraic groups, Pacific J. Math. 130 (1987), no. 2, 253–273.
  5. Doty, Stephen R.; Sullivan, John B., Filtration patterns for representations of algebraic groups and their Frobenius kernels, Math. Z. 195 (1987), no. 3, 391–407.
  6. Doty, Stephen, Composition factors of induced modules for algebraic groups and their Frobenius subgroups, The Arcata Conference on Representations of Finite Groups (Arcata, Calif., 1986), 163–170, Proc. Sympos. Pure Math., 47, Part 2, Amer. Math. Soc., Providence, RI, 1987.
  7. Doty, Stephen R.; Sullivan, John B, On the intertwinings between higher cohomology modules of line bundles on G∕B, J. Algebra 115 (1988), no. 2, 289–296.
  8. Doty, Stephen, The strong linkage principle, Amer. J. Math. 111 (1989), no. 1, 135–141.
  9. Doty, Stephen, Submodules of symmetric powers of the natural module for GLn, Invariant theory (Denton, TX, 1986), 185–191, Contemp. Math., 88, Amer. Math. Soc., Providence, RI, 1989.
  10. Doty, Stephen, Character formulas and Frobenius subgroups of algebraic groups, J. Algebra 125 (1989), no. 2, 331–347.
  11. Doty, Stephen, Filtrations of rational representations of reductive groups of semisimple rank 1, Proc. Amer. Math. Soc. 109 (1990), no. 1, 9–22.
  12. Doty, Stephen, The symmetric algebra and representations of general linear groups, Proceedings of the Hyderabad Conference on Algebraic Groups (Hyderabad, 1989), 123–150, Manoj Prakashan, Madras, 1991.
  13. Doty, Stephen R.; Walker, Grant, The composition factors of Fp[x1,x2,x3] as a GL(3,p)-module, J. Algebra 147 (1992), no. 2, 411–441.
  14. Doty, Stephen; Walker, Grant, Modular symmetric functions and irreducible modular representations of general linear groups, J. Pure Appl. Algebra 82 (1992), no. 1, 1–26.
  15. Doty, S. R., Resolutions of B modules, Indag. Math. (N.S.) 5 (1994), no. 3, 267–283.
  16. Doty, Stephen; Walker, Grant, Truncated symmetric powers and modular representations of GLn, Math. Proc. Cambridge Philos. Soc. 119 (1996), no. 2, 231–242.
  17. Doty, Stephen R.; Nakano, Daniel K.; Peters, Karl M., On infinitesimal Schur algebras, Proc. London Math. Soc. (3) 72 (1996), no. 3, 588–612.
  18. Doty, Stephen R.; Nakano, Daniel K.; Peters, Karl M., Polynomial representations of Frobenius kernels of GL2, Lie algebras and their representations (Seoul, 1995), 57–67, Contemp. Math., 194, Amer. Math. Soc., Providence, RI, 1996.
  19. Doty, Stephen R.; Nakano, Daniel K.; Peters, Karl M., Infinitesimal Schur algebras of finite representation type, Quart. J. Math. Oxford Ser. (2) 48 (1997), no. 191, 323–345.
  20. Doty, Stephen, Polynomial representations, algebraic monoids, and Schur algebras of classical type, J. Pure Appl. Algebra 123 (1998), no. 1-3, 165–199.
  21. Doty, Stephen R.; Nakano, Daniel K., Semisimple Schur algebras, Math. Proc. Cambridge Philos. Soc. 124 (1998), no. 1, 15–20.
  22. Doty, Stephen, Representation theory of reductive normal algebraic monoids, Trans. Amer. Math. Soc. 351 (1999), no. 6, 2539–2551.
  23. Doty, Stephen R.; Erdmann, Karin; Martin, Stuart; Nakano, Daniel K., Representation type of Schur algebras, Math. Z. 232 (1999), no. 1, 137–182.
  24. Doty, Stephen; Giaquinto, Anthony, Generators and relations for Schur algebras, Electron. Res. Announc. Amer. Math. Soc. 7 (2001), 54–62 (electronic).
  25. Doty, Stephen R.; Nakano, Daniel K., Relating the cohomology of general linear groups and symmetric groups, Modular representation theory of finite groups (Charlottesville, VA, 1998), 175–187, de Gruyter, Berlin, 2001.
  26. Doty, Stephen; Giaquinto, Anthony, Presenting Schur algebras, Int. Math. Res. Not. 2002, no. 36, 1907–1944.
  27. Benkart, Georgia; Doty, Stephen, Derangements and tensor powers of adjoint modules for sln. J. Algebraic Combin. 16 (2002), no. 1, 31–42.
  28. Doty, Stephen; Erdmann, Karin; Nakano, Daniel K., Extensions of modules over Schur algebras, symmetric groups, and Hecke algebras, Algebras and Representation Theory 7 (2004), no. 1, 67–99.
  29. Doty, Stephen; Giaquinto, Anthony, Presenting Schur algebras as quotients of the universal enveloping algebra of gl2, Algebras and Representation Theory 7 (2004), no. 1, 1–17.
  30. Doty, Stephen; Henke, Anne, Decomposition of tensor products of modular irreducibles for SL2, Quart. J. Math. Oxford 56 (2005), 179–187 (electronic).
  31. Doty, Stephen, Presenting generalized q-Schur algebras, Representation Theory 7 (2003), 196–213 (electronic).
  32. Doty, Stephen; Erdmann, Karin; Henke, Anne, A generic algebra associated to certain Hecke algebras, J. Algebra 278 (2004), no. 2, 502–531.
  33. Doty, Stephen; New versions of Schur–Weyl duality, pp.  59–71 in Finite Groups 2003 (Proceedings of the Gainseville Conference on Finite Groups), de Gruyter, Berlin, New York 2004.
  34. Doty, Stephen; Giaquinto, Anthony; Sullivan, John B., Presenting Schur algebras in types B, C, D, Advances in Math. 206 (2006), 434–454.
  35. Dipper, Richard; Doty, Stephen, Rational Schur algebras, Represent. Theory 12 (2008), 58–82 (electronic).
  36. Dipper, Richard; Doty, Stephen; Hu, Jun, Brauer’s centralizer algebras, symplectic Schur algebras, and Schur–Weyl duality, Trans. Amer. Math. Soc. 360 (2008), 189–213.
  37. Doty, Stephen; Erdmann, Karin; Henke, Anne, Endomorphism rings of permutation modules over maximal Young subgroups, J. Algebra 307 (2007), 377–396.
  38. Doty, Stephen; Green, R.M., Presenting affine q-Schur algebras, Math. Zeit. 256 (2007), 311–345.
  39. Doty, Stephen, Schur–Weyl duality in positive characteristic, Contemporary Math. 478 (2009), 15-28.
  40. Doty, Stephen; Giaquinto, Anthony; Sullivan, John B., On the defining relations for generalized q-Schur algebras, Advances in Math. 221 (2009), 955-982.
  41. Bowman, Chris; Doty, Stephen; Martin, Stuart, Decomposition of tensor products of modular irreducibles for SL3 (with an Appendix by C.M. Ringel), International Electronic J. Algebra 9 (2011), 177-219. 
  42. Doty, Stephen; Hu, Jun, Schur–Weyl duality for orthogonal groups, Proc. London Math. Soc. (3) 98 (2009), 679-713.
  43. Cox, Anton; DeVisscher, Maud; Doty, Stephen; Martin, Paul P., Semisimplicity and blocks of the rational Brauer algebra in characteristic zero, J. Algebra 320 (2008), 169–212.
  44. Doty, Stephen, Constructing quantized enveloping algebras via inverse limits of finite dimensional algebras,  J. Algebra 321 (2009), 1225-1238.
  45. Doty, Stephen; Martin, Stuart, Hook modules for general linear groups, Archiv der Mathematik (Basel) 92 (2009), 206-214.
  46. Doty, Stephen; Nyman, Kathryn, Annihilators of permutation modules, Quart. J. Math. 62 (2011), no. 1, 87–102.
  47. Benson, David; Doty, Stephen, Schur–Weyl duality over finite fields, Archiv der Mathematik (Basel) 93 (2009), 425-435.
  48. Dipper, Richard; Doty, Stephen; Stoll, Friederike, The quantized walled Brauer algebra and mixed tensor space, Algebras and Representation Theory 17 (2014), no. 2, 675-701.
  49. Dipper, Richard; Doty, Stephen; Stoll, Friederike, Quantized mixed tensor space and Schur–Weyl duality, Algebra Number Theory 7 (2013), no. 5, 1121-1146.
  50. Doty, Stephen, Factoring tilting modules for algebraic groups, J. Lie Theory 19 (2009), 531-535.
  51. Doty, Stephen, Addendum to: "Constructing quantized enveloping algebras via inverse limits of finite dimensional algebras'', J. Algebra 323 (2010), no. 6, 1845-1847.
  52. Doty, Stephen; Giaquinto, Anthony, Cellular bases of generalized q-Schur algebras, Math. Proc. Cambridge Philos. Soc. 162 (2017), no. 3, 533–560. 
  53. Doty, Stephen, A characteristic-free decomposition of tensor space as a Brauer algebra module, J. Lie Theory 22 (2012), no. 3, 869-882. 
  54. Bowman, Chris; Doty, Stephen; Martin, Stuart, Decomposition of tensor products of modular irreducibles for SL3
    the ≥ 5 case, International Electronic J. of Algebra 17 (2015), 105-138.
  55. Doty, Stephen; Li, Yiqiang, A geometric construction of generalized q-Schur algebras, in "Recent Advances in Representation Theory, Quantum Groups, Algebraic Geometry, and Related Topics: AMS Special Sessions on Geometric and Algebraic Aspects of Representation Theory and Quantum Groups, and Noncommutative Algebraic Geometry, October 13-14, 2012, Tulane University, New Orleans, Louisiana", Contemporary Math. 623, American Math. Society 2014.
  56. Doty, Stephen, Representations of reductive normal algebraic monoids, pp 87-96 in "Algebraic Monoids, Group Embeddings, and Algebraic Combinatorics", Fields Inst. Communications 71, Springer 2014.
  57. Doty, Stephen; Douglass, J. Matthew, Schur-Weyl duality and the free Lie algebra, Proc. Amer. Math. Soc. 145 (2017), 3263-3277.
  58. Doty, Stephen; Lauve, Aaron; Seelinger, George H., Canonical idempotents of multiplicity-free families of algebras, preprint 2016; submitted. 
  59. Bowman, Chris; Doty, Stephen; Martin, Stuart, An integral second fundamental theorem of invariant theory for partition algebras, work in progress.
  60. Bowman, Chris; Doty, Stephen; Martin, Stuart, Integral Schur-Weyl duality for partition algebras, work in progress.
Software

Weyl Modules, a GAP package supporting various computations with Weyl modules for semisimple algebraic groups.