Lusztig symmetries and Poincare-Birkhoff-Witt basis for wUr,sd( osp (1|2n))

2013 ◽  
Vol 54 (12) ◽  
pp. 121704 ◽  
Author(s):  
Junli Liu ◽  
Shilin Yang
Keyword(s):  
Witt Basis ◽  
Lusztig Symmetries

scholarly journals Multiplicities of Higher Lie Characters

2003 ◽  
Vol 75 (1) ◽  
pp. 9-21 ◽  
Author(s):  
Manfred Schocker
Keyword(s):  
Symmetric Group ◽  
Associative Algebra ◽  
Free Associative Algebra ◽  
Combinatorial Description ◽  
Irreducible Components ◽  
Witt Basis ◽  
Special Case ◽  
Regular Character

AbstractThe higher Lie characters of the symmetric group Sn arise from the Poincaré-Birkhoff-Witt basis of the free associative algebra. They are indexed by the partitions of n and sum up to the regular character of Sn. A combinatorial description of the multiplicities of their irreducible components is given. As a special case the Kraśkiewicz-Weyman result on the multiplicities of the classical Lie character is obtained.

LUSZTIG SYMMETRIES AND AUTOMORPHISMS OF QUANTUM SUPERALGEBRAS Uq(osp(1|2r))

2010 ◽  
Vol 09 (05) ◽  
pp. 725-762 ◽  
Author(s):  
XUEKUN CHEN ◽  
SHILIN YANG
Keyword(s):  
Hopf Algebra ◽  
Braid Group ◽  
Group Relations ◽  
Lusztig Symmetries ◽  
Quantum Superalgebras

We first construct algebra automorphisms Ti (1 ≤ i ≤ r) of ℤ2-graded Hopf algebra Uq( osp (1|2r)), which are called Lusztig's symmetries. It is shown that they satisfy braid group relations. The algebraic automorphisms of Uq( osp (1|2r)) are also described.

scholarly journals Operads with compatible CL-shellable partition posets admit a Poincaré-Birkhoff-Witt basis

2021 ◽  
pp. 1
Author(s):  
Joan Bellier-Millès ◽  
Bérénice Delcroix-Oger ◽  
Eric Hoffbeck
Keyword(s):  
Witt Basis

Lyndon Words, Free Algebras and Shuffles

1989 ◽  
Vol 41 (4) ◽  
pp. 577-591 ◽  
Author(s):  
Guy Melançon ◽  
Christophe Reutenauer
Keyword(s):  
Pattern Matching ◽  
Lower Central Series ◽  
Free Lie Algebra ◽  
Central Series ◽  
Loop Invariant ◽  
Combinatorial Properties ◽  
Witt Basis ◽  
Lyndon Word ◽  
Conjugation Class ◽  
Lyndon Words

A Lyndon word is a primitive word which is minimum in its conjugation class, for the lexicographical ordering. These words have been introduced by Lyndon in order to find bases of the quotients of the lower central series of a free group or, equivalently, bases of the free Lie algebra [2], [7]. They have also many combinatorial properties, with applications to semigroups, pi-rings and pattern-matching, see [1], [10].We study here the Poincaré-Birkhoff-Witt basis constructed on the Lyndon basis (PBWL basis). We give an algorithm to write each word in this basis: it reads the word from right to left, and the first encountered inversion is either bracketted, or straightened, and this process is iterated: the point is to show that each bracketting is a standard one: this we show by introducing a loop invariant (property (S)) of the algorithm. This algorithm has some analogy with the collecting process of P. Hall [5], but was never described for the Lyndon basis, as far we know.

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