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Map of Science

Green, Richard M.

Professor

Positions

• Professor, Mathematics

Research Areas

• Algebra
• Combinatorics

Research

research overview

• My main areas of interest are algebraic Lie theory and algebraic combinatorics, particularly the combinatorics of Coxeter groups. I am also interested in applications of these theories to other areas of mathematics, and to the sciences.

keywords

• algebraic Lie theory, algebraic combinatorics, combinatorics of Coxeter groups

Publications

selected publications

• book

  • Combinatorics of minuscule representations.  Ed. 199.  2013
    

• chapter

  • On representations of affine Temperley-Lieb algebras.  245-261. 1998

• journal article

  • Positivity Properties for Spherical Functions of Maximal Young Subgroups.  Annals of Combinatorics. 889-908. 2024
  • 2-roots for Simply Laced Weyl Groups.  Transformation Groups. 2023
    
  • Coxeter group actions and limits of hypergeometric series.  The Ramanujan Journal: an international journal devoted to areas of mathematics influenced by Ramanu. 607-651. 2020
  • What is... a Minuscule Representation?.  Notices of the American Mathematical Society. 1-1. 2020
    
  • Classification of Coxeter groups with finitely many elements of $protect mathbf{a}$-value 2.  Algebraic Combinatorics. 331-364. 2020
  The nil Temperley-Lieb algebra of type affine C.  Journal of Pure and Applied Algebra. 4966-4993. 2019
  
  A classification of the Veldkamp lines of the near hexagon L-3 x GQ(2,2).  Ars Mathematica Contemporanea. 287-299. 2017
  Relations among complementary and supplementary pairings of Saalschutzian F-4(3)(1) series.  The Ramanujan Journal: an international journal devoted to areas of mathematics influenced by Ramanu. 647-679. 2016
  THE VELDKAMP SPACE OF THE SMALLEST SLIM DENSE NEAR HEXAGON.  International Journal of Geometric Methods in Modern Physics. 2013
  On the cyclically fully commutative elements of Coxeter groups.  Journal of Algebraic Combinatorics: an international journal. 123-148. 2012
  A PRESENTATION FOR THE SYMPLECTIC BLOB ALGEBRA.  Journal of Algebra and Its Applications. 2012
  Morse matchings on polytopes.  Algebraic and Geometric Topology. 2429-2450. 2012
  Coxeter group actions on F-4(3)(1) hypergeometric series.  The Ramanujan Journal: an international journal devoted to areas of mathematics influenced by Ramanu. 93-128. 2011
  On the Maximally Clustered Elements of Coxeter Groups.  Annals of Combinatorics. 467-478. 2010
  Homology representations arising from the half cube, II.  Journal of Combinatorial Theory: Series A. 1037-1048. 2010
  THE VELDKAMP SPACE OF GQ(2,4).  International Journal of Geometric Methods in Modern Physics. 1133-1145. 2010
  On the combinatorics of Kac's asymmetry function.  Commentationes Mathematicae Universitatis Carolinae. 217-235. 2010
  Homology representations arising from the half cube.  Advances in Mathematics. 216-239. 2009
  Leading coefficients of Kazhdan-Lusztig polynomials and fully commutative elements.  Journal of Algebraic Combinatorics: an international journal. 165-171. 2009
  ON THE MARKOV TRACE FOR TEMPERLEY-LIEB ALGEBRAS OF TYPE E-n.  Journal of Knot Theory and Its Ramifications. 237-264. 2009
  FULL HEAPS AND REPRESENTATIONS OF AFFINE WEYL GROUPS.  International Electronic Journal of Algebra. 1-42. 2008
  REPRESENTATIONS OF LIE ALGEBRAS ARISING FROM POLYTOPES.  International Electronic Journal of Algebra. 27-52. 2008
  Generalized Jones traces and Kazhdan-Lusztig bases.  Journal of Pure and Applied Algebra. 744-772. 2007
  Towers of recollement and bases for diagram algebras: Planar diagrams and a little beyond.  Journal of Algebra. 392-452. 2007
  Presenting affine q-Schur algebras.  Mathematische Zeitschrift. 311-345. 2007
  Constructing cell data for diagram algebras.  Journal of Pure and Applied Algebra. 551-569. 2007
  Presenting affine q-Schur algebras.  Mathematische Zeitschrift. 311-345. 2007
  FULL HEAPS AND REPRESENTATIONS OF AFFINE KAC MOODY ALGEBRAS.  International Electronic Journal of Algebra. 137-188. 2007
  Star reducible Coxeter groups.  Glasgow Mathematical Journal. 583-609. 2006
  Schubert varieties and free braidedness.  Transformation Groups. 327-336. 2004
  Schubert Varieties and Free Braidedness.  Transformation Groups. 327-336. 2004
  Standard modules for tabular algebras.  Algebras and Representation Theory. 419-440. 2004
  Acyclic heaps of pieces, II.  Glasgow Mathematical Journal. 459-476. 2004
  Freely braided elements in Coxeter groups, II.  Advances in Applied Mathematics. 26-39. 2004
  Acyclic heaps of pieces, I.  Journal of Algebraic Combinatorics: an international journal. 173-196. 2004
  Categories arising from tabular algebras.  Glasgow Mathematical Journal. 333-352. 2003
  On planar algebras arising from hypergroups.  Journal of Algebra. 126-150. 2003
  On rank functions for heaps.  Journal of Combinatorial Theory: Series A. 411-424. 2003
  Tabular algebras and their asymptotic versions.  Journal of Algebra. 27-64. 2002
  On 321-avoiding permutations in affine Weyl groups.  Journal of Algebraic Combinatorics: an international journal. 241-252. 2002
  
  Freely braided elements of Coxeter groups.  Annals of Combinatorics. 337-348. 2002
  Decorated tangles and canonical bases.  Journal of Algebra. 594-628. 2001
  Fully commutative Kazhdan-Lusztig cells.  Annales de l'Institut Fourier. 1025-1045. 2001
  A projection property for Kazhdan-Lusztig bases.  International Mathematics Research Notices. 23-23. 2000
  On representations of affine Temperley–Lieb algebras, II.  Pacific Journal of Mathematics. 243-273. 1999
  On the affine Temperley-Lieb algebras.  Journal of London Mathematical Society. 366-380. 1999
  The affine q-Schur algebra.  Journal of Algebra. 379-411. 1999
  
  Canonical bases for Hecke algebra quotients.  Mathematical Research Letters. 213-222. 1999
  Completions of cellular algebras.  Communications in Algebra. 5349-5366. 1999
  Cellular algebras arising from Hecke algebras of type H-n.  Mathematische Zeitschrift. 365-383. 1998
  A matrix setting for the q-Schur algebra.  Journal of London Mathematical Society. 289-308. 1998
  Generalized Temperley-Lieb algebras and decorated tangles.  Journal of Knot Theory and Its Ramifications. 155-171. 1998
  QUANTIZED SYMMETRIC POWERS.  Quarterly Journal of Mathematics. 479-492. 1997
  Quantized symmetric powers.  Quarterly Journal of Mathematics. 479-492. 1997
  Positivity properties for q-Schur algebras.  Cambridge Philosophical Society: Mathematical Proceedings. 401-414. 1997
  Hyperoctahedral Schur algebras.  Journal of Algebra. 418-438. 1997
  Monomials and Temperley-Lieb algebras.  Journal of Algebra. 498-517. 1997
  A diagram calculus for certain canonical bases.  Communications in Mathematical Physics. 521-532. 1997
  q-Schur algebras as quotients of quantized enveloping algebras.  Journal of Algebra. 660-687. 1996
  A straightening formula for quantized codeterminants.  Communications in Algebra. 2887-2913. 1996
  ... more

Teaching

courses taught

• MATH 2001 - Introduction to Discrete Mathematics
  Primary Instructor - Fall 2018 / Fall 2019 / Fall 2022
  Introduces the ideas of rigor and proof through an examination of basic set theory, existential and universal quantifiers, elementary counting, discrete probability, and additional topics. Credit not granted for this course and MATH 2002.
• MATH 2130 - Introduction to Linear Algebra for Non-Mathematics Majors
  Primary Instructor - Spring 2018 / Fall 2021
  Examines basic properties of systems of linear equations, vector spaces, inner products, linear independence, dimension, linear transformations, matrices, determinants, eigenvalues, eigenvectors and diagonalization. Intended for students who do not plan to major in Mathematics. Degree credit not granted for this course and MATH 2135 or APPM 3310. Formerly MATH 3130.
• MATH 2135 - Introduction to Linear Algebra for Mathematics Majors
  Primary Instructor - Fall 2019 / Fall 2020 / Fall 2023 / Summer 2024
  Examines basic properties of systems of linear equations, vector spaces, inner products, linear independence, dimension, linear transformations, matrices, determinants, eigenvalues, eigenvectors and diagonalization. Intended for students who plan to major in Mathematics. Degree credit not granted for this course and MATH 2130 or APPM 3310. Formerly MATH 3135.
• MATH 3140 - Abstract Algebra 1
  Primary Instructor - Spring 2018 / Summer 2018 / Summer 2019 / Fall 2020 / Spring 2022 / Summer 2024 / Fall 2024
  Studies basic properties of algebraic structures with a heavy emphasis on groups. Other topics, time permitting, may include rings and fields.
• MATH 4140 - Abstract Algebra 2
  Primary Instructor - Spring 2023
  Explores some topic that builds on material in MATH 3140. Possible topics include (but are not limited to) Galois theory, representation theory, advanced linear algebra or commutative algebra. Same as MATH 5140.
MATH 5140 - Abstract Algebra 2
Primary Instructor - Spring 2023
Explores some topic that builds on material in MATH 3140. Possible topics include (but are not limited to) Galois theory, representation theory, advanced linear algebra or commutative algebra. Department enforced prerequisite: MATH 3140. Same as MATH 4140.
MATH 6130 - Algebra 1
Primary Instructor - Fall 2021 / Fall 2023
Studies group theory and ring theory. Department enforced prerequisite: MATH 3140. Instructor consent required for undergraduates.
MATH 6140 - Algebra 2
Primary Instructor - Spring 2019 / Spring 2020 / Spring 2021 / Spring 2023
Studies modules, fields and Galois theory. Department enforced prerequisite: MATH 6130. Instructor consent required for undergraduates.
... more

Background

education and training

• M.A., Oxford Univ (England) 1996
• Ph.D., Univ of Warwick (England) 1995
• M.S., Univ of Warwick (England) 1993
• B.A., Oxford Univ (England) 1992

International Activities

geographic focus

• Americas  Transnational Region
• Canada  Country
• China  Country
• Italy  Country
• Japan  Country
Slovakia  Country
United Kingdom  Country
eastern Asia  Transnational Region
eastern Europe  Transnational Region
... more

Other Profiles

ORCID iD

• http://orcid.org/0000-0001-8818-3224

Google Scholar

• https://scholar.google.com/citations?user=lwCoySV1i7MC

ResearchGate

• https://www.researchgate.net/profile/Richard_Green8