کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8896273 | 1630413 | 2018 | 33 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On the second fundamental theorem of invariant theory for the orthosymplectic supergroup
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: On the second fundamental theorem of invariant theory for the orthosymplectic supergroup On the second fundamental theorem of invariant theory for the orthosymplectic supergroup](/preview/png/8896273.png)
چکیده انگلیسی
Let OSp(V) be the orthosymplectic supergroup on an orthosymplectic vector superspace V of superdimension (m|2n). Lehrer and Zhang showed that there is a surjective algebra homomorphism Frr:Br(mâ2n)âEndOSp(V)(Vâr), where Br(mâ2n) is the Brauer algebra of degree r with parameter mâ2n. The second fundamental theorem of invariant theory in this setting seeks to describe the kernel KerFrr of Frr as a 2-sided ideal of Br(mâ2n). In this paper, we show that KerFrrâ 0 if and only if râ¥rc:=(m+1)(n+1), and give a basis and a dimension formula for KerFrr. We show that KerFrr as a 2-sided ideal of Br(mâ2n) is generated by KerFrcrc for any râ¥rc, and we provide an explicit set of generators for KerFrcrc. These generators coincide in the classical case with those obtained in recent papers of Lehrer and Zhang on the second fundamental theorem of invariant theory for the orthogonal and symplectic groups. As an application we obtain the necessary and sufficient conditions for the endomorphism algebra Endosp(V)(Vâr) over the orthosymplectic Lie superalgebra osp(V) to be isomorphic to Br(mâ2n).
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 501, 1 May 2018, Pages 394-434
Journal: Journal of Algebra - Volume 501, 1 May 2018, Pages 394-434
نویسندگان
Yang Zhang,