An updated version of my Indian Parties list, with some more info:
Indian National Congress
Originally the main purveyors of the independence movement, after dominionization, the Indian National Congress became more concerned with autonomy within the AFS Commonwealth, joining the People's Alliance to ensure that Indian interests are properly represented. At first, it was one of the more left-leaning of the PA cadet parties, even going through conflict on occasion with the main PA. However, after the '79 Crisis, the party underwent a rightward shift. The left dwindled, expelled from the party, and a new influx of members belonging to the RSS and other Hindu nationalist parties replaced them. These new members adopted a hardline anti-Communist, pro-capitalist stance, ensuring India remained firmly in the Capitalist sphere. It also began to pursue policies supporting conservative social policies and favoring Hindus and other "Dharmic faiths" (Sikhism, Buddhism, Jainism). The common joke in modern times is that the INC is now the political arm of the RSS. Their policies helped transform India into the beating heart of the capitalist sphere, surpassing even Western Europe and the main Franco-British Union. However, even in this new capitalist leader, there are systemic problems of poverty, corruption, persistence of the caste system, environmental degradation, religious tension, and ethnic nationalism, which threatens to shake the INC rule, and destroy capitalism's last hope. Despite ramblings that cracks in Indian capitalism are growing, reformists hope to solve the systemic problems of India, while maintaining its status as the rising leader of capital.
The INC retains the support of the affluent and upper class, upper caste Hindus, royalty in the Princely States, and especially Hindu nationalists and conservatives. Its support base primarily lies in the North and Nepal, and in more conservative rural regions in the South.
The current leader of the party, and the Prime Minister of the Greater Indian Commonwealth, is Narendra Modi, the latest in a line of RSS members in charge of the party. Despite his heavy anti-Communist stance, he has expressed his desire for reforming the system in order for India to better survive in a modern world.
All-India Muslim League
Founded in 1906, the All-India Muslim League is the main political party for the Muslim minority. After spending the 1930's advocating a separate Muslim state in Muslim majority areas, negotiations between Congress head B.R. Ambedkar and party head Muhammad Ali Jinnah eventually forced the League to abandon this notion. They instead returned to their roots as a Muslim advocacy group, going into coalition with the INC to ensure that the Commonwealth recognize Muslim interests and rights. However, with the rise of the RSS as a major faction in the INC, and the subsequent Hindutva policies it pursued, the League has cut off its alliance, and became a major regional force in its own right. While still being pro-capitalist, it advocates more for Muslim rights and autonomy (especially in the face of increased persecution), which precludes the possibility of the League joining with the Socialists and Communists in their reformist agenda. However, there is a growing Islamic Social Democratic wing of the party more willing to work with the opposition against the homogeneity of INC rule. While the reactionary portion of the party has begun to return to Sir Muhammad's Iqbal's idea of a separate Islamic state, the mainstream realize that remaining part of India is in their best interest, primarily because the proposed state would be split between two sides of the country.
Support largely centers around Muslim majority areas, such as the Northwest regions (Punjab, Sindh, Balochistan) and the Bengali states. They enjoy the support of affluent Muslims and Muslim nationalists.
The current party head is Newaz Sharif
Indian Socialist Congress
Founded by dissident factions of the Indian National Congress after the founding of the Commonwealth, the Socialist Congress has taken up the mantle of full-on independence from the FBU and the AFS, albeit through legal, not revolutionary, means. It is a cadet party of the Labour Party, and follows Fabian socialism and social democracy. Through several common goals with the INC, they had managed to hold some influence in the country during its early days, helped by its moderate stance. However, this ended after 1979, when socialist politicians were arrested and/or persecuted, forcing them from office in many cases. This struck a blow to the party. However, it largely absorbed the left of the Congress Party during the crisis, expanding their base. In recent years, the Socialists have begun to advocate a reformist agenda, which includes reformist socialism, Dalit rights, detente with Comintern (and generally against military actions in the Indian Ocean against communism) and environmentalism. These stances, along with a calculated media image, became popular with a new generation of people, who are tired of capitalism, and want India to move away from dying ideologies.
Support for the Socialist Congress lies in working class and impoverished urban communities, college campuses, and the intellectual community
The current head of the Party is Rahul Gandhi, great-grandson of Jawaharal Nehru, one of the founders of the Indian Socialist Congress.
The Worker's Communist Party of India
Originally simply "The Communist Party of India", it was founded in 1920. Originally following Marxist-Leninism, the party was significantly changed by the joining of radical Bhagat Singh in 1947, who brought the party more to a Marxist-DeLeonist/Trotskyist model. The name change was meant to reflect the "Worker's Communist Party of America." They joined Comintern as a party around 1952, and became part of the pro-American faction of the alliance. It was one of the only Communist parties to remain relatively above ground in the AFS during the entirety of the Cold War, despite it adopting militant tactics at times during its history. Even during the Emergency period, they avoided an outright ban, though it was heavily persecuted during that time. After the anti-communist hysteria died down, The Communist Party moderated some of its militancy, and following their colleagues in ESCI, formed a leftist coalition with the Socialist Congress to enact a reformist agenda, sharing common goals, including the elimination of the caste system and environmentalism. Together, they hope to create a socialist state in India slowly and peacefully. It is considered "Left-Wing" on the Comintern spectrum.
It holds major support among urban radicals and lower caste peoples (especially Dalits). The Party also commands support among certain nationalists who dislike the overly centralized GIC government (which makes token gestures towards ethnic autonomy through certain created states, but still welds most of the power), but don't want to break off from India entirely for various reasons. Historically, it has been successful in Central India, Burma, and the South.
The current leader of the Worker's Communist Party is Sitram Yechury, a former student organizer, and later major party member.
The Communist Party of India (Zapatismo)
Formed from a split in the Worker's Communist Party in 1978, it was initially a very small faction, advocating Zapatismo, peasant led revolution. However, after the moderation of the main Communist party, support had grown for this faction. It is the dissident from the "Left Consensus", desiring to advocate change more forcefully. While not resorting to outright terrorism and (very carefully) avoid outright advocating the overthrow of the government , they often organize armed strikes in rural communities and factories, causing friction with the government. Besides this, they also organize schools and literacy programs in these communities, teaching them the tenants of communism and the evils of the caste system. Of the Left opposition, they are the most outspoken in both leaving the AFS, and military policing in the Indian Ocean. However, they are not a member of Comintern, and have on various occasions denounced it, preferring to use their own methods and ideology.
The Z-Communist Party is too radical for many Indian leftists, who tend to gravitate to the more moderate "Left Consensus" of the Socialist Congress and the mainstream Communist Party. Still, its independent programs of rural literacy have gained it a following in many poorer rural areas. It has become very popular on college campuses, where their symbol is often plastered on walls, despite the attempts of school officials.
The current head is Muppalla Lakshmana Rao, a former radical.
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Following
@WotanArgead 's example, I might do Parties of Japan.