Quiver-graded Richardson orbits

References

• Assem, I., Simson, D., Skowroński, A. (2006). Elements of the Representation Theory of Associative Algebras. Vol. 1, Techniques of representation theory. London Mathematical Society Student Texts, vol. 65, Cambridge: Cambridge University Press.
   Google Scholar
• Baur, K. (2005). A normal form for admissible characters in the sense of Lynch. Represent. Theory 9:30–45.
   Google Scholar
• Baur, K. (2006). Richardson elements for classical Lie algebras. J. Algebra 297(1):168–185.
   Web of Science ®Google Scholar
• Baur, K., Goodwin, S. M. (2008). Richardson elements for parabolic subgroups of classical groups in positive characteristic. Algebr. Represent. Theory 11(3):275–297.
   Web of Science ®Google Scholar
• Brüstle, T., Hille, L. (2000). Finite, tame, and wild actions of parabolic subgroups in GL(V) on certain unipotent subgroups. J. Algebra 226(1):347–360.
   Web of Science ®Google Scholar
• Brüstle, T., Hille, L., Ringel, C. M., Röhrle, G. (1999). The Δ-filtered modules without self-extensions for the Auslander algebra of k[T]/〈Tn〉. Algebr. Represent. Theory 2(3):295–312. DOI: 10.1023/A:1009999006899.
   Google Scholar
• Babson, E., Huisgen-Zimmermann, B., Thomas, R. (2009). Generic representation theory of quivers with relations. J. Algebra 322(6):1877–1918.
   Web of Science ®Google Scholar
• Birkhoff, G. (1935). Subgroups of abelian groups. Proc. Lond. Math. Soc. s2-38(1):385–401. DOI: 10.1112/plms/s2-38.1.385.
   Google Scholar
• Bongartz, K. (1983). Algebras and quadratic forms. J. Lond. Math. Soc. (2) 28(3):461–469. DOI: 10.1112/jlms/s2-28.3.461.
   Google Scholar
• Crawley-Boevey, W., Schröer, J. (2002). Irreducible components of varieties of modules. J. Reine Angew. Math. 553:201–220.
   Web of Science ®Google Scholar
• Crawley-Boevey, W., Sauter, J. (2017). On quiver Grassmannians and orbit closures for representation-finite algebras. Math. Z. 285(1-2):367–395. DOI: 10.1007/s00209-016-1712-z.
   Web of Science ®Google Scholar
• Conde, T., Erdmann, K. (2018). The Ringel dual of the Auslander–Dlab–Ringel algebra. J. Algebra 504:506–535. DOI: 10.1016/j.jalgebra.2018.02.029.
   Web of Science ®Google Scholar
• Cohn, P. M. (1991). Algebra. vol. 3, Chichester: Wiley.
   Google Scholar
• Conde, T. (2016). The quasihereditary structure of the Auslander-Dlab-Ringel algebra. J. Algebra 460:181–202.
   Web of Science ®Google Scholar
• Dlab, V., Ringel, C. M. (1992). The module theoretical approach to quasi-hereditary algebras. In: Representations of Algebras and Related Topics (Kyoto, 1990), London Math. Soc. Lecture Note Ser., vol. 168, Cambridge: Cambridge University Press, pp. 200–224.
   Google Scholar
• Eiríksson, Ö. (2017). From submodule categories to the stable auslander algebra. J. Algebra 486:98–118.
   Web of Science ®Google Scholar
• Eiríksson, Ö. (2018). Quasi-hereditary algebras and the geometry of representations of algebras, Ph.D. thesis, Bielefeld: Universität Bielefeld.
   Google Scholar
• Franjou, V., Pirashvili, T. (2004). Comparison of abelian categories recollements. Doc. Math 9:41–56.
   Google Scholar
• Gabriel, P. (1972). Unzerlegbare darstellungen i. Manuscr. Math. 6(1):71–103. DOI: 10.1007/BF01298413.
   Google Scholar
• Gabriel, P. (1975). Finite representation type is open. In Representations of Algebras. Springer Lecture Notes in Mathematics 488. Berlin: Springer, pp. 132–155.
   Google Scholar
• Christof, G. (1996). Geometric methods in representation theory of finite-dimensional algebras. In: Representation Theory of Algebras and Related Topics (Mexico City, 1994), CMS Conf. Proc., vol. 19, Providence, RI: American Mathematical Society, pp. 53–63.
   Google Scholar
• Goodwin, S. M., Hille, L. (2007). Prehomogeneous spaces for Borel subgroups of general linear groups. Transform. Groups 12(3):475–498.
   Web of Science ®Google Scholar
• Hille, L., Röhrle, G. (1999). A classification of parabolic subgroups of classical groups with a finite number of orbits on the unipotent radical. Transform. Groups 4(1):35–52. DOI: 10.1007/BF01236661.
   Web of Science ®Google Scholar
• Jensen, B. T., Su, X., Yu, R. W. T. (2009). Rigid representations of a double quiver to type A, and Richardson elements in seaweed Lie algebras. Bull. Lond. Math. Soc. 41(1):1–15. DOI: 10.1112/blms/bdn087.
   Google Scholar
• Kuhn, N. J. (1994). Generic representations of the finite general linear groups and the Steenrod algebra. II. K-Theory 8(4):395–428. DOI: 10.1007/BF00961409.
   Google Scholar
• Lusztig, G. (1991). Quivers, perverse sheaves, and quantized enveloping algebras. J. Amer. Math. Soc. 4(2):365–421. DOI: 10.1090/S0894-0347-1991-1088333-2.
   Google Scholar
• Pressland, M., Sauter, J. Special tilting modules for algebras with positive dominant dimension. arXiv:1705.03367, May 2017.
   Google Scholar
• Reineke, M. (2003). Quivers, desingularizations and canonical bases. In: Studies in Memory of Issai Schur (Chevaleret/Rehovot, 2000), Progress in Mathematics, 210, Boston, MA: Birkhäuser, pp. 325–344.
   Google Scholar
• Richardson, R. W. Jr., (1974). Conjugacy classes in parabolic subgroups of semisimple algebraic groups. Bull. Lond. Math. Soc. 6(1):21–24. DOI: 10.1112/blms/6.1.21.
   Google Scholar
• Ringel, C. M. (2010). Iyama’s finiteness theorem via strongly quasi-hereditary algebras. J. Pure Appl. Algebra 214(9):1687–1692.
   Web of Science ®Google Scholar
• Ringel, C. M., Schmidmeier, M. (2006). Submodule categories of wild representation type. J. Pure Appl. Algebra 205(2):412–422. DOI: 10.1016/j.jpaa.2005.07.002.
   Web of Science ®Google Scholar
• Ringel, C. M., Schmidmeier, M. (2008). The Auslander-Reiten translation in submodule categories. Trans. Amer. Math. Soc. 360(2):691–716 (electronic).
   Google Scholar
• Sauter, J. (2014). Springer theory and the geometry of quiver flag varieties, Ph.D. thesis. Leeds: University of Leeds.
   Google Scholar
• Simson, D. (2007). Representation types of the category of subprojective representations of a finite poset over and a solution of a Birkhoff type problem. J. Algebra 311(1):1–30. DOI: 10.1016/j.jalgebra.2007.01.029.
   Web of Science ®Google Scholar
• Simson, D. (2015). Tame–wild dichotomy of Birkhoff type problems for nilpotent linear operators. J. Algebra 424:254–293.
   Web of Science ®Google Scholar
• Slodowy, P. (1980). Simple Singularities and Simple Algebraic Groups, vol. 815, Lecture Notes in Mathematics. Berlin: Springer.
   Google Scholar
• Varagnolo, M., Vasserot, E. (2011). Canonical bases and KLR-algebras. J. Reine Angew. Math. 659:67–100.
   Web of Science ®Google Scholar
• Xiong, B.-L., Zhang, P., Zhang, Y.-H. (2014). Auslander–Reiten translations in monomorphism categories. Forum Math. 26(3):863–912.
   Web of Science ®Google Scholar
• Zwara, G. (2002). Smooth morphisms of module schemes. Proc. Lond. Math. Soc. (3) 84(3):539–558. DOI: 10.1112/S0024611502013382.
   Google Scholar