## Shi regions in type A2

Shi regions in type A2

## Shi regions in type B2

Shi regions in type B2

## Shi regions in type G2

Shi regions in type G2

## Shi regions in type A2 seen in the Tits cone

Shi regions in type A2 seen in the Tits cone

## Shi regions in type B2 seen in the Tits cone

Shi regions in type B2 seen in the Tits cone

## Poset of Shi regions in type A2

Poset of Shi regions in type A2

## Orientations of Alcoves in type A2

Orientations of Alcoves in type A2

## Parameterization of alcoves in type A2

Parameterization of alcoves in type A2

## Minimal elements of Shi regions in type B2

Minimal elements of Shi regions in type B2

## Descent process between Shi regions and dominant Shi regions in type B2

Descent process between Shi regions and dominant Shi regions in type B2

## Minimal element of a Shi region in type G2 seen in the projective representation of roots

Minimal element of a Shi region in type G2 seen in the projective representation of roots

## Another minimal element of a Shi region in type G2 seen in the projective representation of roots

Another minimal element of a Shi region in type G2 seen in the projective representation of roots

## Irreducible components of the Shi variety in type A2

Irreducible components of the Shi variety in type A2

## Irreducible components of the Shi variety in type B2

Irreducible components of the Shi variety in type B2

## Fundamental polytope in type B2

Fundamental polytope in type B2

## Alcoves of the fundamental polytope in type G2 seen as set of representatives of the irreducible components of the Shi variety in type G2

Alcoves of the fundamental polytope in type G2 seen as set of representatives of the irreducible components of the Shi variety in type G2

## Bijection between the components in type A3 and the circular permutations of A3

Bijection between the components in type A3 and the circular permutations of A3

## Bijection between the components in type A4 and the circular permutations of A4

Bijection between the components in type A4 and the circular permutations of A4

## Circular lines diagram of (164235)

Circular lines diagram of (164235)

## Linear lines diagram of (164235)

Linear lines diagram of (164235)

## Algorithm via linear lines diagrams to obtain the circular permutation corresponding to the Shi vector given

Algorithm via linear lines diagrams to obtain the circular permutation corresponding to the Shi vector given

## Irreducible components of the Shi variety in type B3 seen with the Shi vectors in the fundamental polytope

Irreducible components of the Shi variety in type B3 seen with the Shi vectors in the fundamental polytope

## Irreducible components of the Shi variety in type A4 and link with Young's lattice

Irreducible components of the Shi variety in type A4 and link with Young's lattice

## Irreducible components of the Shi variety in type A5 and link with Young's lattice

Irreducible components of the Shi variety in type A5 and link with Young's lattice

## Triangulations of a 5-gon via admitted Shi vectors

Triangulations of a 5-gon via admitted Shi vectors

## Parenthesizations of a word with 4 letters and corresponding triangulations of the pentagon. Both figures are a representation of the associahedron of type A2.

Parenthesizations of a word with 4 letters and corresponding triangulations of the pentagon. Both figures are a representation of the associahedron of type A2.

## Associahedron corresponding to the quiever 1 --> 2 <-- 3 (figure made by Emine Yildirim)

Associahedron corresponding to the quiever 1 --> 2 <-- 3 (figure made by Emine Yildirim)

## Hasse diagram of the Bruhat order of A3

Hasse diagram of the Bruhat order of A3

## Hasse diagram of the Bruhat order of A4

Hasse diagram of the Bruhat order of A4

## Hasse diagram of the Bruhat order of B3

Hasse diagram of the Bruhat order of B3

## Strip geometry of the partition 2>1>1

Strip geometry of the partition 2>1>1