Abstract
We present an algorithm which computes the annihilator in \({\mathrm {U}}(\mathfrak {sl}(\infty ))\) of any simple highest weight \(\mathfrak {sl}(\infty )\)-module \(L_{\mathfrak {b}}(\lambda )\). This algorithm is based on an infinite version of the Robinson–Schensted algorithm.
To Anthony Joseph on the occasion of his 75th birthday
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Acknowledgements
We thank Professors Maria Gorelik and Anna Melnikov for inviting us to participate and present the results of this paper at the sister conferences in Israel celebrating Anthony Joseph’s 75th birthday. We are grateful to Professor Anthony Joseph for his kind attention to our work. Both authors have been supported in part by DFG grant PE 980/6-1, and the second author has been supported in part by RFBR grant 16-01-00818.
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Penkov, I., Petukhov, A. (2019). Primitive Ideals of \({\mathrm {U}}(\mathfrak {sl}(\infty ))\) and the Robinson–Schensted Algorithm at Infinity. In: Gorelik, M., Hinich, V., Melnikov, A. (eds) Representations and Nilpotent Orbits of Lie Algebraic Systems. Progress in Mathematics, vol 330. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-23531-4_13
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