Decompose the tensor square of the type-A2 letter crystal¶
Continuously checked
This is the exact source run by make test-examples and the ordinary Python test gate.
Domains: combin
Source: examples/23_kashiwara_crystals.py
# SPDX-License-Identifier: MIT
# Copyright (c) 2026 Benjamin Antieau and Deven Manam
"""Decompose the tensor square of the type-A2 letter crystal."""
from noether.combin import KashiwaraCrystal
def main() -> None:
letters = KashiwaraCrystal.type_a_letters(2)
tensor_square = letters.tensor(letters)
highest_weights = sorted(
tensor_square.weight(vertex) for vertex in tensor_square.highest_weight_vertices()
)
assert tensor_square.vertex_count == 9
assert highest_weights == [(0, 1), (2, 0)]
print(f"B(omega_1)^2 has highest weights {highest_weights}")
if __name__ == "__main__":
main()