Raising/Lowering Maps and Modules for the Quantum Affine Algebra

@inproceedings{FunkNeubauer2005RaisingLoweringMA,
  title={Raising/Lowering Maps and Modules for the Quantum Affine Algebra},
  author={Darren Funk-Neubauer},
  year={2005}
}
Let V denote a finite dimensional vector space over an algebraically closed field. Let U 0, U 1,…, U d denote a sequence of nonzero subspaces whose direct sum is V. Let R:V → V and L:V → V denote linear transformations with the following properties: for 0 ≤ i ≤ d, R U i  ⊆ U i+1 and L U i  ⊆ U i−1 where U −1 = 0, U d+1 = 0; for 0 ≤ i ≤ d/2, the restrictions R d−2i | U i : U i  → U d−i and L d−2i | U d−i : U d−i  → U i are bijections; the maps R and L satisfy the cubic q-Serre relations where q… CONTINUE READING

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