Let G be a special linear group over the real,the complex or the quaternion,or a special unitary group.In this note,we determine all special unipotent representations of G in the sense of Arthur and Barbasch-Vogan,and...Let G be a special linear group over the real,the complex or the quaternion,or a special unitary group.In this note,we determine all special unipotent representations of G in the sense of Arthur and Barbasch-Vogan,and show in particular that all of them are unitarizable.展开更多
In this article,by studying the Bernstein degrees and Goldie rank polynomials,we es-tablish a comparison between the irreducible representations of G=GL_(n)(C)possessing the minimal Gelfand-Kirillov dimension and thos...In this article,by studying the Bernstein degrees and Goldie rank polynomials,we es-tablish a comparison between the irreducible representations of G=GL_(n)(C)possessing the minimal Gelfand-Kirillov dimension and those induced from finite-dimensional representations of the maximal parabolic subgroup of G of type(n-1,1).We give the transition matrix between the two bases for the corresponding coherent families.展开更多
This paper proposes a novel continuous variable coherent optical communication mode. In this mode, two quadrature Stokes parameters are regarded as observed physical quantity, and single linearly polarized component i...This paper proposes a novel continuous variable coherent optical communication mode. In this mode, two quadrature Stokes parameters are regarded as observed physical quantity, and single linearly polarized component is used as carrier wave. At the sending end, electro-optical amplitude modulator （EOM） of 45° azimuth is used to indirectly complete the linear modulation of S2 component, and S3 component is changed by continuously rotating a half-wave plate （HWP）. The receiving end adopts the mode of Q-Q-H wave plate are rotated to select the component of measured S2 or S3. The circuit of balance homodyne detection is designed, and the detection system is built by combination with LabVIEW to complete signal demodulation. New optical path scheme is verified by both theory and experiment.展开更多
基金supported by NSF grant (Award Number 2000254)supported by the National Natural Science Foundation of China (Grant Nos. 11701364 and 11971305)+4 种基金Xiamen University Malaysia Research Fund (Grant No. XMUMRF/2022-C9/IMAT/0019)supported by National Key R&D Program of China (Grant Nos. 2022YFA1005300 and 2020YFA0712600)New Cornerstone Investigator Programsupported by MOE AcRF Tier 1 grant A-0004280-00-00Provost’s Chair grant E-146-000-052-001 in NUS
文摘Let G be a special linear group over the real,the complex or the quaternion,or a special unitary group.In this note,we determine all special unipotent representations of G in the sense of Arthur and Barbasch-Vogan,and show in particular that all of them are unitarizable.
基金Z.Bai was supported in part by the National Natural Science Foundation of China(Grant No.12171344)the National Key R&D Program of China(Grant Nos.2018YFA0701700 and 2018YFA0701701)+5 种基金Y.Chen was supported in part by the National Natural Science Foundation of China(Grant No.12301035)the Natural Science Foundation of Jiangsu Province(Grant No.BK20221057)D.Liu was supported by National Key R&D Program of China(Grant No.2022YFA1005300)the National Natural Science Foundation of China(Grant No.12171421)B.Sun was supported by National Key R&D Program of China(Grant Nos.2022YFA1005300 and 2020YFA0712600)New Cornerstone Investigator Program。
文摘In this article,by studying the Bernstein degrees and Goldie rank polynomials,we es-tablish a comparison between the irreducible representations of G=GL_(n)(C)possessing the minimal Gelfand-Kirillov dimension and those induced from finite-dimensional representations of the maximal parabolic subgroup of G of type(n-1,1).We give the transition matrix between the two bases for the corresponding coherent families.
基金This work was supported by the National Natural Science Foundation of China （Grant No. 61177072）.
文摘This paper proposes a novel continuous variable coherent optical communication mode. In this mode, two quadrature Stokes parameters are regarded as observed physical quantity, and single linearly polarized component is used as carrier wave. At the sending end, electro-optical amplitude modulator （EOM） of 45° azimuth is used to indirectly complete the linear modulation of S2 component, and S3 component is changed by continuously rotating a half-wave plate （HWP）. The receiving end adopts the mode of Q-Q-H wave plate are rotated to select the component of measured S2 or S3. The circuit of balance homodyne detection is designed, and the detection system is built by combination with LabVIEW to complete signal demodulation. New optical path scheme is verified by both theory and experiment.
