R - matrix

Basis of H ( Grote war, Ew Grad )

Entry e- Groo) = I EH# (Grid )

csm ( Dicarlo ) = Za- t f EHF ( Grif )csm ( re Gr, E) = z

,-t t tr

can ( rnc Grad'

) = I C- HE ( Grad )

Csm (Dq e- Groo) = I.

Csm classeswith "

opposite"

En (D ,car

,I ) = za- t

reference flagdm ( re Gr, E) = z

,-t t tr

can ( re Grady = i fdm (to e- Groo) = I

y em (r ,car, I ) = Zz- t th

vscsm ( re Gr, E) = Z

,-t

can ( rnc Grad'

) = I

Calculation : change of basis matrix :

"⇒* I:÷÷÷÷÷÷÷÷÷÷.= z.IE#eItddtz.E+hlB.P

Fact this matrix satisfies the

parameter- dependent Yang - Baxter equation :

Riz (Zi -E) 12,3ft , - Zz) Raz (E-Zz)=Rz3(E-Zz ) Rb ft , - Zz)Raft , -Ze)(verify ! ! ! )

€: " "" "

÷:÷÷÷±÷÷¥¥Exo E I → d- ④ E ④ €2

Rig. (z) acts as Rte ) in i' th & g-'

th factor

"

Ruth-Z) "

RodEZz)

:

I\

, I

ft .-H =3 L ;

1213 -2 22

Further along this direction . ..

this particular solution of the TB equationis the R -matrix of Y ( gla )

Yangiau

→ HE ( Y Gruen ) is a Ylgk )-module

(with CSI classes playingthe role of standardbasis vectors )

"

spin basis"