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• W2963235664 abstract "We compare two important bases of an irreducible representation of the symmetric group: the web basis and the Specht basis. The web basis has its roots in the Temperley–Lieb algebra and knot-theoretic considerations. The Specht basis is a classic algebraic and combinatorial construction of symmetric group representations which arises in this context through the geometry of varieties called Springer fibers. We describe a graph that encapsulates combinatorial relations between each of these bases, prove that there is a unique way (up to scaling) to map the Specht basis into the web representation, and use this to recover a result of Garsia–McLarnan that the transition matrix between the Specht and web bases is upper-triangular with ones along the diagonal. We then strengthen their result to prove vanishing of certain additional entries unless a nesting condition on webs is satisfied. In fact we conjecture that the entries of the transition matrix are nonnegative and are nonzero precisely when certain directed paths exist in the web graph." @default.
• W2963235664 created "2019-07-30" @default.
• W2963235664 creator A5028867644 @default.
• W2963235664 creator A5037445253 @default.
• W2963235664 date "2017-08-03" @default.
• W2963235664 modified "2023-10-02" @default.
• W2963235664 title "The Transition Matrix between the Specht and Web Bases Is Unipotent with Additional Vanishing Entries" @default.
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• W2963235664 doi "https://doi.org/10.1093/imrn/rnx164" @default.
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