Type C ^ Brauer loop schemes and loop model with boundaries
Annales de l’Institut Henri Poincaré D, Tome 3 (2016) no. 2, pp. 163-255.

In this paper we study the Brauer loop model on a strip and the associated quantum Knizhnik–Zamolodchikov (qKZ) equation. We show that the minimal degree solution of the Brauer qKZ equation with one of four di�erent possible boundary conditions, gives the multidegrees of the irreducible components of generalizations of the Brauer loop scheme of [16, Knutson–Zinn-Justin ’07] with one of four kinds of symplectic-type symmetry. This is accomplished by studying these irreducible components, which are indexed by link patterns, and describing the geometric action of Brauer generators on them. We also provide recurrence relations for the multidegrees and compute the sum rules (multidegrees of the whole schemes).

Accepté le :
Publié le :
DOI : 10.4171/aihpd/28
Classification : 82-XX, 14-XX, 81-XX
Mots-clés : Brauer algebra, quantum Knizhnik–Zamolodchikov equation, equivariant cohomology, Loop model 
@article{AIHPD_2016__3_2_163_0,
     author = {Ponsaing, Anita and Zinn-Justin, Paul},
     title = {Type $\widehat{\mathrm C}$ {Brauer} loop schemes and loop model with boundaries},
     journal = {Annales de l{\textquoteright}Institut Henri Poincar\'e D},
     pages = {163--255},
     volume = {3},
     number = {2},
     year = {2016},
     doi = {10.4171/aihpd/28},
     mrnumber = {3506076},
     zbl = {1348.82031},
     language = {en},
     url = {http://archive.numdam.org/articles/10.4171/aihpd/28/}
}
TY  - JOUR
AU  - Ponsaing, Anita
AU  - Zinn-Justin, Paul
TI  - Type $\widehat{\mathrm C}$ Brauer loop schemes and loop model with boundaries
JO  - Annales de l’Institut Henri Poincaré D
PY  - 2016
SP  - 163
EP  - 255
VL  - 3
IS  - 2
UR  - http://archive.numdam.org/articles/10.4171/aihpd/28/
DO  - 10.4171/aihpd/28
LA  - en
ID  - AIHPD_2016__3_2_163_0
ER  - 
%0 Journal Article
%A Ponsaing, Anita
%A Zinn-Justin, Paul
%T Type $\widehat{\mathrm C}$ Brauer loop schemes and loop model with boundaries
%J Annales de l’Institut Henri Poincaré D
%D 2016
%P 163-255
%V 3
%N 2
%U http://archive.numdam.org/articles/10.4171/aihpd/28/
%R 10.4171/aihpd/28
%G en
%F AIHPD_2016__3_2_163_0
Ponsaing, Anita; Zinn-Justin, Paul. Type $\widehat{\mathrm C}$ Brauer loop schemes and loop model with boundaries. Annales de l’Institut Henri Poincaré D, Tome 3 (2016) no. 2, pp. 163-255. doi : 10.4171/aihpd/28. http://archive.numdam.org/articles/10.4171/aihpd/28/

Cité par Sources :