Geodesic
Parabolic extension of Hecke ring of the general linear group.~II
Zapiski Nauchnykh Seminarov POMI, Modular functions and quadratic forms. Part 1, Tome 183 (1990), pp. 56-76

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Hecke rings of parabolical subgroups of the general linear group axe investigated. The decompositions of the standard polynomial and the skew-symmetric square of the standard polynomial are calculated. Such decompositions are used in the theory of modular forms. 
@article{ZNSL_1990_183_a3,
     author = {V. A. Gritsenko},
     title = {Parabolic extension of {Hecke} ring of the general linear {group.~II}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {56--76},
     publisher = {mathdoc},
     volume = {183},
     year = {1990},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1990_183_a3/}
}
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V. A. Gritsenko. Parabolic extension of Hecke ring of the general linear group.~II. Zapiski Nauchnykh Seminarov POMI, Modular functions and quadratic forms. Part 1, Tome 183 (1990), pp. 56-76. http://geodesic.mathdoc.fr/item/ZNSL_1990_183_a3/