scholarly journals COMBINATORICS OF CANONICAL BASES REVISITED: STRING DATA IN TYPE A

2021 ◽  
Author(s):  
V. GENZ ◽  
G. KOSHEVOY ◽  
B. SCHUMANN
Keyword(s):  
Crystal Structure ◽  
Type A ◽  
Explicit Description ◽  
Special Choice ◽  
Canonical Bases ◽  
Integer Points ◽  
Reduced Word ◽  
Reduced Words

AbstractWe give a formula for the crystal structure on the integer points of the string polytopes and the *-crystal structure on the integer points of the string cones of type A for arbitrary reduced words. As a byproduct, we obtain defining inequalities for Nakashima–Zelevinsky string polytopes. Furthermore, we give an explicit description of the Kashiwara *-involution on string data for a special choice of reduced word.

scholarly journals Combinatorics of canonical bases revisited: type A

2021 ◽  
Vol 27 (4) ◽  
Author(s):  
Volker Genz ◽  
Gleb Koshevoy ◽  
Bea Schumann
Keyword(s):  
Type A ◽  
Canonical Bases

scholarly journals A Crystal on Decreasing Factorizations in the 0-Hecke Monoid

10.37236/9168 ◽  
2020 ◽  
Vol 27 (2) ◽  
Author(s):  
Jennifer Morse ◽  
Jianping Pan ◽  
Wencin Poh ◽  
Anne Schilling
Keyword(s):  
Crystal Structure ◽  
Symmetric Group ◽  
Type A ◽  
Young Tableaux

We introduce a type $A$ crystal structure on decreasing factorizations of fully-commu\-tative elements in the 0-Hecke monoid which we call $\star$-crystal. This crystal is a $K$-theoretic generalization of the crystal on decreasing factorizations in the symmetric group of the first and last author. We prove that under the residue map the $\star$-crystal intertwines with the crystal on set-valued tableaux recently introduced by Monical, Pechenik and Scrimshaw. We also define a new insertion from decreasing factorization to pairs of semistandard Young tableaux and prove several properties, such as its relation to the Hecke insertion and the uncrowding algorithm. The new insertion also intertwines with the crystal operators.

Darstellung und Kristallstruktur von Ba10Al3Ge7 / Preparation and Crystal Structure of Ba10Al3Ge7

1977 ◽  
Vol 32 (6) ◽  
pp. 619-624 ◽  
Author(s):  
Axel Widera ◽  
Herbert Schäfer
Keyword(s):  
Crystal Structure ◽  
Intermetallic Compound ◽  
Type A ◽  
Structure Type

The new intermetallic compound Ba10Al3Ge7 crystallizes hexagonal in a new structure type (a = 974.9(5) pm, c =1647(1) pm, c/a = 1.69, P63/mcm). The Al-atoms, together with the Ge-atoms, form propeller-like Al3Ge7-units.

scholarly journals Affine type A geometric crystal structure on the Grassmannian

2020 ◽  
Vol DMTCS Proceedings, 28th... ◽  
Author(s):  
Gabriel Frieden
Keyword(s):  
Crystal Structure ◽  
Type A ◽  
Young Tableaux ◽  
Rectangular Shape ◽  
International Audience ◽  
Affine Type

International audience We construct a type A(1) n−1 affine geometric crystal structure on the Grassmannian Gr(k, n). The tropicalization of this structure recovers the combinatorics of crystal operators on semistandard Young tableaux of rectangular shape (with n − k rows), including the affine crystal operator e 0. In particular, the promotion operation on these tableaux essentially corresponds to cyclically shifting the Plu ̈cker coordinates of the Grassmannian.

Canonical bases of modified quantum algebras for type A2

2018 ◽  
Vol 17 (06) ◽  
pp. 1850113
Author(s):  
Weideng Cui
Keyword(s):  
Canonical Basis ◽  
Quantum Algebra ◽  
Explicit Description ◽  
Quantum Algebras ◽  
Canonical Bases ◽  
Type Formula

The modified quantum algebra [Formula: see text] associated to a quantum algebra [Formula: see text] was introduced by Lusztig. [Formula: see text] has a remarkable basis, which was defined by Lusztig, called the canonical basis. In this paper, we give an explicit description of all elements of the canonical basis of [Formula: see text] for type [Formula: see text].

scholarly journals The Co-crystal Structure of Staphylococcal Enterotoxin Type A With Zn2+at 2.7 Å Resolution

1996 ◽  
Vol 271 (50) ◽  
pp. 32212-32216 ◽  
Author(s):  
Michael Sundström ◽  
Dan Hallén ◽  
Anders Svensson ◽  
Elinor Schad ◽  
Mikael Dohlsten ◽  
...  
Keyword(s):  
Crystal Structure ◽  
Type A ◽  
Staphylococcal Enterotoxin

scholarly journals Coxeter-Knuth Graphs and a Signed Little Map for Type B Reduced Words

10.37236/4384 ◽  
2014 ◽  
Vol 21 (4) ◽  
Author(s):  
Sara Billey ◽  
Zachary Hamaker ◽  
Austin Roberts ◽  
Benjamin Young
Keyword(s):  
Structure Theorem ◽  
Type A ◽  
Axiomatic Characterization ◽  
Schubert Calculus ◽  
Type B ◽  
Dual Equivalence ◽  
Carry Over ◽  
Dual Equivalence Graphs ◽  
Reduced Words

We define an analog of David Little’s algorithm for reduced words in type B, and investigate its main properties. In particular, we show that our algorithm preserves the recording tableau of Kraśkiewicz insertion, and that it provides a bijective realization of the Type B transition equations in Schubert calculus. Many other aspects of type A theory carry over to this new setting. Our primary tool is a shifted version of the dual equivalence graphs defined by Assaf and further developed by Roberts. We provide an axiomatic characterization of shifted dual equivalence graphs, and use them to prove a structure theorem for the graph of Type B Coxeter-Knuth relations. 

Sign in / Sign up

Export Citation Format

Share Document