Universität zu Köln > Mathematisches Institut > Arbeitsgruppe Algebra

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Research Interests

Some (Pre-) Publications

• P. Littelmann: Über Horns Vermutung, Geometrie, Kombinatorik und Darstellungstheorie. (German) [On Horn's conjecture, geometry, combinatorics and representation theory], Jahresber. Deutsch. Math.-Verein. 110 (2008), no.2, 75-99
• P. Littelmann, H.-J. Sommers, M. R. Zirnbauer: Superbosonization of invariant random matrix ensembles, Comm. Math. Phys. 283 (2008), no. 2, 343-395
• G. Fourier, P. Littelmann: Weyl modules, affine Demazure modules, fusion products and limit constructions
  
• G. Fourier, P. Littelmann: Tensor product structure of affine Demazure modules and limit constructions, Nagoya Math. Journal
  
• S. Gaussent, P. Littelmann: LS-galleries, the path model and MV-cycles, Duke Math. J. 127 (2005), no. 1, 35--88.
• P. Littelmann: Bases for representations, LS-paths and Verma flags A tribute to C. S. Seshadri (Chennai, 2002), 323--345, Trends Math., Birkhäuser, Basel, 2003
• P. Caldero, P. Littelmann: Adapted bases and standard monomial theory J. Pure Appl. Algebra 191 (2004), no. 1-2, 99--118
• V. Lakshmibai, P. Littelmann: Richardson varieties and equivariant $K$-theory. J. Algebra 260 (2003), no. 1, 230--260
• S. Kumar, P. Littelmann: Algebraization of Frobenius splitting via quantum groups  Ann. of Math. (2) 155 (2002), no. 2, 491--551
  
• V. Lakshmibai, P. Littelmann, P. Magyar: Standard Monomial Theory for Bott-Samelson Varieties, Compositio Math.130, 293--318 (2001)
• P. Littelmann, C.S. Seshadri: Pieri-Chevalley type formula for $K(G/B)$ and standard monomial theory. Studies in memory of Issai Schur (Chevaleret/Rehovot, 2000), 155--176, Progr. Math., 210, Birkhäuser Boston, Boston, MA, 2003.
• S. Kumar, P. Littelmann: Frobenius splitting in characteristic zero and the quantum Frobenius map, J.Pure Appl. Algebra (2000).
• P. Littelmann: Contracting Modules and Standard Monomial Theory for Symmetrizable Kac-Moody Algebras, JAMS 11, (1998), pp. 551--567.
• P. Littelmann: Cones, crystals and patterns, Transf. Groups 3, (1998), pp. 145--179.
• P. Littelmann: Bases canoniques et applications, S\'eminaire Bourbaki, 50\`eme ann\´ee, no 847 (1998).
•  P. Littelmann: The path model, the quantum Frobenius map and Standard Monomial Theory, ``Algebraic Groups and Their Representations'' (R. Carter and J. Saxl, eds.), Kluwer Academic Publishers (1998).
• V. Lakshmibai, P. Littelmann, P. Magyar: Standard Monomial Theory and applications, ``Representation Theories and Algebraic Geometry'' (A. Broer, ed.), Kluwer Academic Publishers (1998).
• P. Littelmann: Characters of representations and paths in ${h}_{\R}^*$, Proceedings of Symposia in Pure Mathematics 61, (1997), pp. 29--49.
• P. Littelmann: A plactic algebra for semisimple Lie algebras, Advances in Mathematics 124 (1996), pp. 312--331
• P. Littelmann: Paths and root operators in representation theory, Annals of Mathematics 142, 1995, pp. 499--525.
• P. Littelmann: A Littlewood-Richardson type rule for symmetrizable Kac-Moody algebras, Inventiones mathematicae 116 (1994)
• P. Littelmann: The path model of representations, Proceedings of the ICM Zürich 1994, Birkhäuser Verlag, Basel--Boston, 1995, pp. 298--308.

Popularizing Publication

• P. Littelmann: Jeu de taquin et tableaux de Young, erschienen in der Zeitschrift  L'Ouvert (1999)

Teaching

Wintersemester 2009/2010:

• Vorlesung: Mathematik für Physiker I
  
• Seminar: Kombinatorische Modelle der Darstellungstheorie
  
• Arbeitsgruppe Algebra
  

Sommersemester 2009:

• Vorlesung: Algebraische Geometrie
  
• Vorlesung: Affine Grassmannvarietät und Satakeisomorphismus
  
• Proseminar: Young Tableaux: Kombinatorik und Darstellungstheorie
  
• Arbeitsgruppe Algebra
  

Further Information

   Graduiertenkolleg:

   Coorganizer of the seminar Transformation Groups and Mathematical Physics

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