This book gives a systematic account of the structure and representation theory of finite-dimensional complex Lie superalgebras of classical type and serves as a good introduction to representation theory of Lie superalgebras. Several folklore results are rigorously proved (and occasionally corrected in detail), sometimes with new proofs. Three important dualities are presented in the book, with the unifying theme of determining irreducible characters of Lie superalgebras. In order of increasing sophistication, they are Schur duality, Howe duality, and super duality. The combinatorics of symmetric functions is developed as needed in connections to Harish-Chandra homomorphism as well as irreducible characters for Lie superalgebras. Schur-Sergeev duality for the queer Lie superalgebra is presented from scratch with complete detail. Howe duality for Lie superalgebras is presented in book form for the first time. Super duality is a new approach developed in the past few years toward understanding the Bernstein-Gelfand-Gelfand category of modules for classical Lie superalgebras. Super duality relates the representation theory of classical Lie superalgebras directly to the representation theory of classical Lie algebras and thus gives a solution to the irreducible character problem of Lie superalgebras via the Kazhdan-Lusztig polynomials of classical Lie algebras.

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This open access book delves into discussions central to hydraulic structures and research in the realm of hydrodynamics. Hydraulic structures stand as pivotal components within civil engineering and construction, playing a safeguarding role for structures vital to human development. Examples encompass the Hoover Dam in the USA, the Three Gorges Dam in China and the Almendra Dam in Salamanca, Spain. Monitoring the safety and ensuring the structural stability of hydraulic structures has long remained a focal point within hydraulic engineering. Factors affecting the safety of hydraulic structures, water pressure, and loading demand meticulous attention. The stability of structures and materials experiences degradation due to hydraulic impact and long-term corrosion, compromising the safety of hydraulic structures. The inability to adequately support and release water during flood season or flooding can result in irreversible damage. The book aims to furnish global civil engineers with cutting-edge research and engineering examples pertaining to the safety and hydrodynamics of hydraulic structures, with a particular emphasis on dam safety and inspection. It endeavors to inspire novel insights and research avenues for the readers and provide some experiences and results for disciplinary research in this field. The topics of this book include but are not limited to the following:1. Structural Safety and Intelligent Monitoring of Dams2. Study of Hydraulic Soil Stability and Seepage Effects3. Hydrodynamic Characterization and Flood Control System Construction

This book gives a systematic account of the structure and representation theory of finite-dimensional complex Lie superalgebras of classical type and serves as a good introduction to representation theory of Lie superalgebras. Several folklore results are rigorously proved (and occasionally corrected in detail), sometimes with new proofs. Three important dualities are presented in the book, with the unifying theme of determining irreducible characters of Lie superalgebras. In order of increasing sophistication, they are Schur duality, Howe duality, and super duality. The combinatorics of symmetric functions is developed as needed in connections to Harish-Chandra homomorphism as well as irreducible characters for Lie superalgebras. Schur-Sergeev duality for the queer Lie superalgebra is presented from scratch with complete detail. Howe duality for Lie superalgebras is presented in book form for the first time. Super duality is a new approach developed in the past few years toward understanding the Bernstein-Gelfand-Gelfand category of modules for classical Lie superalgebras. Super duality relates the representation theory of classical Lie superalgebras directly to the representation theory of classical Lie algebras and thus gives a solution to the irreducible character problem of Lie superalgebras via the Kazhdan-Lusztig polynomials of classical Lie algebras.

View the abstract.

This open access book delves into discussions central to hydraulic structures and research in the realm of hydrodynamics. Hydraulic structures stand as pivotal components within civil engineering and construction, playing a safeguarding role for structures vital to human development. Examples encompass the Hoover Dam in the USA, the Three Gorges Dam in China and the Almendra Dam in Salamanca, Spain. Monitoring the safety and ensuring the structural stability of hydraulic structures has long remained a focal point within hydraulic engineering. Factors affecting the safety of hydraulic structures, water pressure, and loading demand meticulous attention. The stability of structures and materials experiences degradation due to hydraulic impact and long-term corrosion, compromising the safety of hydraulic structures. The inability to adequately support and release water during flood season or flooding can result in irreversible damage. The book aims to furnish global civil engineers with cutting-edge research and engineering examples pertaining to the safety and hydrodynamics of hydraulic structures, with a particular emphasis on dam safety and inspection. It endeavors to inspire novel insights and research avenues for the readers and provide some experiences and results for disciplinary research in this field. The topics of this book include but are not limited to the following:1. Structural Safety and Intelligent Monitoring of Dams2. Study of Hydraulic Soil Stability and Seepage Effects3. Hydrodynamic Characterization and Flood Control System Construction