Journal of Lie Theory

no. 2
Alpha-Determinant Cyclic Modules of gln(C)
Journal of Lie Theory, Volume 16 (2006) no. 2, pp. 393-405
The alpha-determinant unifies and interpolates the notion of the determinant and permanent. We determine the irreducible decomposition of the cyclic module of $\frak{gl}_n({\Bbb C})$ defined by the alpha-determinant. The degeneracy of the irreducible decomposition is determined by the content polynomial of a given partition.
DOI: 10.5802/jolt.416
Classification: 06B15, 15A15
Keywords: Schur module, Young symmetrizer, permanent, Frobenius notation, irreducible decomposition, cyclic module 
@article{JOLT_2006_16_2_a10,
     author = {S. Matsumoto and M. Wakayama},
     title = {Alpha-Determinant {Cyclic} {Modules} of {gl\protect\textsubscript{n}(C)}},
     journal = {Journal of Lie Theory},
     pages = {393--405},
     year = {2006},
     volume = {16},
     number = {2},
     doi = {10.5802/jolt.416},
     zbl = {1102.17004},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.416/}
}
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S. Matsumoto; M. Wakayama. Alpha-Determinant Cyclic Modules of gln(C). Journal of Lie Theory, Volume 16 (2006) no. 2, pp. 393-405. doi: 10.5802/jolt.416

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