## Rudolf Tange's Homepage

Dr. R.H. Tange
School of Mathematics
University of Leeds
LS2 9JT, Leeds, UK
Office: 9.20
tel. office: +44 (0)113 343 9246
tel. secretariat: +44 (0)113 343 5101
email: R.H.Tange "AT" leeds.ac.uk
my departmental page
Leeds algebra page

### Research Interests

Elementary problems in representation theory, invariant theory, algebraic geometry and ring theory arising from Lie (pron. Lee") theory in positive characteristic.

### Publications and Preprints

• On the first restricted cohomology of a reductive Lie algebra and its Borel subalgebras, Preprint. pdf-file
• with A.Dent, Bases for spaces of highest weight vectors in arbitrary characteristic, Preprint. pdf-file
• Embeddings of spherical homogeneous spaces in characteristic p, Math. Zeit. 288 (2018), no. 1-2, 491–508. pdf-file
• Highest weight vectors and transmutation, to appear in Transform. Groups. pdf-file
• Highest weight vectors for the adjoint action of GL_n on polynomials, II, Transform. Groups 20 (2015), no. 3, 817-830. pdf-file
• Highest weight vectors for the adjoint action of GL_n on polynomials, Pac. J. Math. 258 (2012), no. 2, 497-510. pdf-file
• On embeddings of certain spherical homogeneous spaces in prime characteristic, Transform. Groups. 17 (2012), no. 3, 861-888. pdf-file
• Factorisation properties of group scheme actions, Math. Zeit. 271 (2012), no. 1-2, 157-165. pdf-file
• A bideterminant basis for a reductive monoid, J. Pure and Applied Algebra. 216 (2012), no. 5, 1207-1221. pdf-file
• The Zassenhaus variety of a reductive Lie algebra in positive characteristic, Adv. in Math. 224 (2010), no. 1, 340-354. pdf-file
• with S.Donkin, The Brauer algebra and the symplectic Schur algebra, Math. Zeit. 265 (2010), no. 1, 187-219. pdf-file
• The symplectic ideal and a double centraliser theorem, J. London Math. Soc. 77 (2008), no. 3, 687-699. pdf-file
• Infinitesimal invariants in a function algebra, Canad. J. Math. 61 (2009), no.4, 950-960. pdf-file
• The centre of quantum sl_n at a root of unity, J.Algebra 301 (2006), no.1, 425-445. pdf-file
Remark: The erratum in J.Algebra 302 (2006), no.2, 897-898, is a typographical erratum to the printed version of this paper. J.Algebra is the author of it, not me.
• with A.Premet, Zassenhaus varieties of general linear Lie algebras, J.Algebra 294 (2005), no.1, 177-195. pdf-file
• with M.Bate, B.Martin and G.Roehrle, Closed orbits and uniform S-instability in geometric invariant theory, Trans. Amer. Math. Soc. 365 (2013), no. 7, 3643-3673. pdf-file
• with M.Bate, B.Martin and G.Roehrle, Complete reducibility and conjugacy classes of tuples in algebraic groups and Lie algebras, Math. Zeit. 269 (2011), no.3, 809-832. pdf-file
• with M.Bate, B.Martin and G.Roehrle, Complete reducibility and separability, Trans. Amer. Math. Soc. 362 (2010), no. 8, 4283-4311. pdf-file