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Abstract
The Specht ideal of shape λ, where λ is a partition, is the ideal generated by all Specht polynomials of shape λ. Haiman and Woo proved that these ideals are reduced and found their universal Gröbner bases. In this short note, we give a short proof for these results.
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Acknowledgments
This work was started at the MFO-RIMS Tandem Workshop “Symmetries on polynomial ideals and varieties” at the Mathematisches Forschungsinstitut Oberwolfach (MFO) and the Research Institute for Mathematical Sciences (RIMS). We thank MFO and RIMS for their kind hospitality. The first author is partially supported by KAKENHI 21K03190. The second author is partially supported by KAKENHI 18H01134. The third author is partially supported by KAKENHI 19K03456. We thank professors Yasuhide Numata, Kosuke Shibata, Akihito Wachi and Junzo Watanabe for useful discussions on this project.