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Sage's tensor product rule for crystals differs from that of Kashiwara and Nakashima by reversing the order of the tensor factors. Sage produces the same crystals of tableaux as Kashiwara and Nakashima. With Sage's convention, the tensor product of crystals is the same as the monoid operation on tableaux and hence the
Title, Crystallizing the hypoplactic monoid: from quasi-Kashiwara operators to the Robinson-Schensted-Knuth-type correspondence for quasi-ribbon tableaux. Publication Type, Journal Article. Year of Publication, 2017. Authors, Cain AJ, Malheiro A. Journal, J. Algebr. Comb. Volume, 45. Pagination, 475–524.
The Lusztig involution on a finite-dimensional highest weight crystal B(?) of highest weight ? maps the highest weight vector to the lowest weight vector and the Kashiwara operator fi to ei?, where i? is defined as ?i?=?w0(?i). Here w0 is the longest element of the Weyl group acting on the i-th simple root ?i. EXAMPLES:.
Feb 18, 2011 The goal is to find a basis of a representation V of Uq(g) such that the Kashiwara operators CEi,. CFi act by partial permutations. This will allow us to “draw" V (?) as a colored directed graph. However, simple calculations show that this is impossible, even for the adjoint representation of sl3. But, in a sense
Masaki Kashiwara is a Japanese mathematician. He was a student of Mikio Sato at the University of Tokyo. Kashiwara made leading contributions towards algebraic analysis, microlocal analysis, D-module theory, Hodge theory, sheaf theory and representation theory. Kashiwara and Sato established the foundations of the
A user manual for Cr | A description of CrystalView, Using the web interface, the user can see the tableau associated a vertex of the crystal by moving the mouse pointer over it. When running this program locally (as Additionaly, Kashiwara operators may be applied to the tableaux. All calculations on tableaux are
tableaux in the specified crystal. This can be used to carry out calculations on crystals, including searches for tableaux with specified properties. Additionaly, Kashiwara operators may be applied to the tableaux. All calculations on tableaux are carried out using python. Image files are automatically generated. PostScript.
and the affine crystal operators are defined as e0 = ? ? e1 ? ? and f0 = ? ? f1 ? ? with ? as defined in .. By (2.7), the Xn-crystal structure of Br,s is fixed, that is, all Kashiwara operators ei and fi for 1 ? i ? n are [7] B. Fuchssteiner, et al., MuPAD User's Manual—MuPAD, Version 1.2.2, John Wiley and Sons, Chichester, New.
Feb 9, 2017 Abstract: Kashiwara's crystal graphs have a natural monoid structure that arises by identifying words labelling vertices that appear in the same position of isomorphic components. The celebrated plactic monoid (the monoid of Young tableaux), arises in this way from the crystal graph for the -analogue of the
Feb 19, 2013 Abstract: For types and we prove that the rigged configuration bijection intertwines the classical Kashiwara operators on tensor products of the arbitrary Kirillov-Reshetikhin crystals and the set of the rigged configurations. Comments: v2: 108 pages, the author's final version for publication, Proposition 33

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March 2018