gtPatterns -- a list of Gelfand-Tsetlin patterns of shape lambda

Usage:

gtPattern(lambda)
Inputs:
- lambda, a list,
Outputs:
- L, a list,

Description

Currently only supported for $\mathfrak{g} = sl_n$.

This function computes a list of Gelfand-Tsetlin patterns of shape $\lambda$ by computing the lattice points of the Gelfand-Tsetlin polytope. See the documentation for GTPattern and gtPolytope for more details.

i1 : gtPatterns("A",{2,0,0})

o1 = {{2, 0, 0, 2, 0, 2}, {2, 0, 0, 2, 0, 1}, {2, 0, 0, 2, 0, 0}, {2, 0, 0,
     ------------------------------------------------------------------------
     1, 0, 1}, {2, 0, 0, 1, 0, 0}, {2, 0, 0, 0, 0, 0}}

o1 : List

We compare this to the lattice points of the Gelfand-Tsetlin polytope for this shape.

i2 : P = gtPolytope("A",{2,0,0})

o2 = P

o2 : Polyhedron

i3 : latticePoints(P)

o3 = {| 2 |, | 2 |, | 2 |, | 2 |, | 2 |, | 2 |}
      | 0 |  | 0 |  | 0 |  | 0 |  | 0 |  | 0 |
      | 0 |  | 0 |  | 0 |  | 0 |  | 0 |  | 0 |
      | 0 |  | 1 |  | 1 |  | 2 |  | 2 |  | 2 |
      | 0 |  | 0 |  | 0 |  | 0 |  | 0 |  | 0 |
      | 0 |  | 0 |  | 1 |  | 0 |  | 1 |  | 2 |

o3 : List

Ways to use gtPatterns:

gtPatterns(String,List)

For the programmer

The object gtPatterns is a method function.

The source of this document is in LieAlgebraRepresentations/documentation.m2:2316:0.